suppose-1500-is-initially-invested-in-an-account-and-the-value-of-the-account-grows-exponentially--2

Question

Suppose $\$ 1500$ is initially invested in an account and the value of the account grows exponentially. If the investment doubles in 8 yr, then the amount in the account $t$ years after the initial investment is given by $A(t)$
$$A(t)=1500(2)^{1 / 8}$$
a. Find the amount in the account after 5 yr.
b. Find the amount in the account after 10 yr.
c. Find $A(0)$ and $A(8)$ and interpret the answers in the context of this problem.

Ankit Gupta · Accepted Answer

Nation E. That is the initial investment at a function of time. It is 1500 times to raise the ball T divide by eight Party of discussion. Find a Mountain Amount account After five years of when time is five years, it&#x27;s just 1500 times to listen or five behind by eight. So what you with that? If you use the camp later. Five days to the part eight. We should write it as two recent for 55 Divide Way eight years, 0.625 1500 times to rate about 2.6 to faith and to raise the power wind 6 to 5. We have 1.5 for two times, 1500 is 2313.316 and it is dollars. Next part of the solution. He after Dainius 1500 times to raise to power. 10. Divide by eight and to raise the bar. 10. Divide by eight. We should right then divided by eight is 1.25 to raise two. Part 1.25 It&#x27;s 2.378 times. 1500 that is 3567 in dollar. It is 35 67 6 to 1 box CEO of this question Is it 18 is the Reuben Itwas initial time. So time is zero that is stirring time 1500 times to raise to power the door divide way it that is $1500. So that is initial investment and e off eight. It is 1500 things to raise the bar. Eight. Divide weight, that is, Teddy told him. Dolar it is ticked at investment doubles after eight years.

Ankit Gupta · Answer

$1000 is initially investor an investment e at a function off time. It is given as one culture. It is in the shit that is $1000 initial investment to raise to the bubble dying t divide myself. Food party. Find a month pay pond after five years. So well, do you slave you so 1000 times to raise To report five The wordplay seven, which is 25 divided by seven, is how much? 0.71 for 22 raised to the power do 2.7. Why be weird? Way seven bulls four point 5714 Okay, so or plain. So you did wrong. Five divided by seven is 0.714 to basically about what? 0.714 James one tells her we&#x27;re getting 164 0.34 What would be find them on in the count off for 10 years. So when time is 10 years, it is when tells in times to rest. About what time? 10 by seven. So then by seven ISS 1.4285 to raise about 1.48 way, James one does it that is 2691 Don&#x27;t 66 no, no and foot mark seat And these are units $7 party A zero and a seven and interpret the answer in context off this problem. So here, for easier it is one told it. When time is there to reach to power zero divided by seven artist Tozser $100 that is, It was the initial investment. And for e seven, which is 1000 things to raise reports that when the world was seven that this to raise the bar wondered, is 2000 dollar. So it is. It is 200. That means investment Woods after seventies.

Amrita Bhasin · Answer

this question asked us to give unit and interpreter answer in terms of the balance in the given account. What we know is that the balance, the re average rate of change of the balance is Delta bi over Delta T. Obviously, Delta means change. This look of went to 1000 times 1.8 to the power of five minus 1/5 minutes here, which is obviously just divide by five. This is Oakland went to $93.87 per years. Four units are dollars per year. Now what we know is that this balance on the account increases by an average of this amount in dollars per year.

Clarissa Noh · Answer

Hey, it&#x27;s clear. So when you&#x27;re in here So the amount a accumulated after $1000 is invested for two years on an interest rate of 4% then it could be used with this equation. So for parquet, we have to find the amount accumulated after five years and 10 years. So for T equals five, we got $1217. We&#x27;re going to do the same thing for 10. When we got $1480 for a part B. The original investment was $1000 so we have to find the ear when it accumulated to become 3000. So we just plug in 3000. You got one point through four equals. The T equals three. We&#x27;re gonna take a log of both sides. So we got T equals 28 years for the original investment to trip

Jerry Zhang · Answer

this problem states that a deposit of $10,000 is made in an account that earns 8.5% interest compounded quarterly run. It gives you the function for this $10,000 that makes an 8.5% interest compounded quarter. So he says it&#x27;s a end, or the amount after any quarters is excuse me $10,000 times one plus 0.85 which is 8.5% over four. This part to the power end, where enemies 12 and trees and so on. Integers representing the number of quarters Your money is in the account. So Partner says, read the 1st 8 terms on the secret meeting for the 1st 8 terms, or 8/4 after this money is deposited, how much money is in the account? So all we have to do is substitute the numbers one through eight into this function for N. So if you plug this into your calculator, your 10,000 times one plus point elite five over for power of one, and so that equals 10,000 200 and 12.5. Then if we do the same thing for two all we have to do is replace this one right here with a two. So let&#x27;s not make you confused. So we were right in. Here, too. Is 10,429 0.5. Remember, this is all in dollars, and then free is 10,651 $0.1 before is 10,877 $0.5. Five is 11,108 $0.6. Six is 11,344 $60.7. Uh, that&#x27;s right. Seven up here seven is 11,585 $70.8 and last but not least, eight right here is 11,832 dollars. So remember that all of these are amounts in dollars end quarters or one through 8/4 after the money has been deposited in the account. So let&#x27;s move on to party, Herbie says. Find the balance in the account after 10 years by computing the 40th term from the sequence. So remember that end is in quarters and therefore quarters per year, so it asks us to do the 40th quarter by plugging in 40 friend. So all we have to do is write 10,000 hunch one plus 10.85 over four to the power of 40. And if you value it, evaluate that with your calculator. You&#x27;ll get 23,000 $189.4 So that is the amount of money if you don&#x27;t touch it, and interest rate remains the same after 10 years. So now we move on to part see currency states. That is the balance after 20 years, twice the balance after 10 years and explain, So 20 years is 80 quarters, so that means N would be 80 in 10 years would mean 40 quarters. That means N would be 40. So we&#x27;ve already calculated the balance in the account after 10 years, and then we could calculate the balance in the account after 20. But that is not absolutely necessary because if we look the point 085 or the interest is compound and compound means that it&#x27;s based on the previous value. Instead of the original value. It was based on the original valley, then the amount would increase by exactly the same amount each quarter and therefore each year. However, because it is calm, pounded increases more and more over time. So if you look at quarter one, you see that it&#x27;s 10,212 0.5. That means that from quarter zero to quarter one, it increased by 212 $25 been quick between quarter one to increased by more than $212.5. Because the difference between this milieu and this value is more than 212.5, that means each year there&#x27;s more and more and more money at it to the count, and that amount that is added is more than the was added the previous quarter. So therefore, we can safely say that the answer to Part C is no because interest is compound, that&#x27;s it.

Julian Wong · Answer

problem. We&#x27;re being told that we are investing £1000 in an account that is earning 4.5% interest compounded continuously in part A. They want us to determine how much is in the account after 10 years and after 20 years. So we&#x27;re just changing the value of teeth for 10 years. That would be 1000 times E to the 10000.45 time to the power of 10 times 10. And that would give us £1223.23 for 10 years. So in 10 years and for 20 years we would do the same calculation. Except we changed the value of tea to 20. So in a calculator E to the power of 0.45 times 20 sometimes when 1000. That would give us Ah, £2459.60 in 20 years and park be We are asked to ah, graph this function. So, uh, we just paste this in. This is our graph. Get the right size and ah, we&#x27;re being asked to use this graph to find how long it takes for initial of investment to double to £2000 when we started with £1000 that&#x27;s this point here. £2000 would be, ah, line at White was 2000 and we can see that it intersects at 15.403 as the ah ex Valley or T value in this case. So it takes us, uh, 15.4 years to double our money. Um, alternatively, we could have calculated it using the equation. If we set f V is 2000 then maybe 2000 equals 1000 e to the 10000.45 tea and Ah, yes, I know we haven&#x27;t learned logs yet, so t we can&#x27;t really sell for But if we got the exponential part by itself, meaning we divide both sides by 1000 it would be two equals e to the 20.45 to the power of tea. And I&#x27;m gonna leave it like that because I&#x27;m gonna use this to do part. See, Part C is asking us if we invest £5000 into the account. How long will it take? The double? So if we started with 5000 everything else is the same 0.45 t is the exponents. Ah, if we&#x27;re talking about how long it takes to double 5000 then we&#x27;re really talking about a future value of 10,000 and the process would be the same. We would divide both sides by 5000 to get the exponential part by itself, and we would be left with two equals e to the 20.45 t notice that this equation solving part C was actually the same equation as part beat. It was still too equals to, um this exponential part and in part B, we got the answer 15.4 years. That means, in part, see, solving the same equation would give us t equals 15.4 years. And, ah, the answer to part D, um, or B and C the same. Well, yes, Parts B and C have the same answer. And the reason why is because the doubling time, because doubling time, meaning we just, ah, take the initial value, multiply it by two when we try to isolate the exponential part on the left side of the equation will always have this same value to that represents Dublin because doubling time is independent independent, which means it doesn&#x27;t depend on the initial value, our initial amount. So regardless of how much you started with if you were to ah, calculators doubling time, it will always be the same.

Problem

Graph the functions on your calculator to support…

Problem 50 Hard Difficulty

Answer

a. $A(5)=2313 \cdot 32$ and $A(10)=3567 \cdot 62$
b. $A(0)=\$ 1000,$ is the initial insetment and
$A(8)=\$ 3000,$ is the time taken to double the money

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a. $A(5)=2313 \cdot 32$ and $A(10)=3567 \cdot 62$b. $A(0)=\$ 1000,$ is the initial insetment and$A(8)=\$ 3000,$ is the time taken to double the money

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Caleb E.

Maria G.

Kristen K.

Michael J.

Absolute Value - Example 1

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Julie Miller, Molly O'Neill, Nancy Hyde Intermediate Algebra

Caleb E.

Maria G.

Kristen K.

Michael J.

a. $A(5)=2313 \cdot 32$ and $A(10)=3567 \cdot 62$
b. $A(0)=\$ 1000,$ is the initial insetment and
$A(8)=\$ 3000,$ is the time taken to double the money

Julie Miller, Molly O'Neill, Nancy Hyde

Intermediate Algebra