Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

For how long must $\$ 900$ be left on deposit at $7.3 \%$ compounded quarterly to reach a total accumulation of $\$ 2350 ?$

$$13 y 3 m 7 d$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

Idaho State University

Lectures

03:46

For how long must $\$ 700$…

03:16

For how long must $\$ 2200…

02:50

For how long must $\$ 1700…

01:48

If $\$ 1,300$ is deposite…

02:08

Finding Time If John inves…

02:10

Use a calculator to help s…

05:22

If $\$ 1000$ is invested i…

00:32

How long will it take for …

Here's another problem where we're looking at a principal problem. It's the same formula for all compounded. That's not continuously the difference. Those they changed the word to quarterly. So your principal that you're putting in this $900? So that's P. This time our interest rate is 7.3. So as you move the decimal or twice you get 0.73 we're compounding quarterly. That's four times a year. Four quarters make a dollar. Um, you know, that's a quarterly means, and we want to see how much time it takes to get up to 23 50. So as we're going to solve this, the first step would be to get rid of that 900. So you divide the 900 over, um, and then it's up to you if you want to do a log or natural. But you do the same sign on both sides. I like to do log, though I don't know, just habit. The whole reason for that is I could move this fourty in front eso I'm looking at four t log of that one plus 10.7 3/4, right? So if I'm trying to solve for T because it's just a giant multiplication problem. I mean, I lead the left side alone. That log of 23. 50 over 900. I'm gonna go to a calculator here shortly. I have to divide by both the four and the log of that one plus 10.73 over four Eso. Yeah, you're gonna hear me Type away my calculator. Um, change some numbers around. It's a log of 23. 50 over 900 divided by four. Log of one plus 10.0 73 over four. Make sure you put in parentheses where necessary. Make sure you know how to use your calculator and the decimals. 13.267 And this is in years now. Some teachers might not want that decimal. What they might want is that you write out 13 years. Well, to figure out how many months, what you could do is truncate that number. So we're just looking at the 130.267 You can easily do that with your calculator by subtracting 13 and then if you multiply by 12 because there's 12 months in a year, you get 3.207 So that would be, uh, three months and then again, truncate, You know, subtract off that three and take that 0.207 I don't know if you multiply by 30 or 31. Um, I'll just multiply by 30 to say it's about six days. Um, if you multiply by 31 I'm sure it's going to be more like seven days. Um, and some people might even argue that if you write down six days, but it's not quite there yet, you have to wait till the seventh day to get to that answer. Eso. I mean, I commit with seven days. Hopefully, that makes sense.

View More Answers From This Book

Find Another Textbook

Numerade Educator

00:59

$f(x, y)=100 x^{1 / 4} y^{3 / 4},$ determine (a) $f(1,16),(\text { b) } f(16…

03:36

The population is growing at about $6 \%$ each year. If the population in 20…

01:23

Solve for $x$ in.$$16^{3 x+1}=64^{2-5 x}$$

05:06

Find the area of the triangle formed by the $x$ -axis and the tangent lines …

01:13

Use the properties of logarithms to find the derivative. Hint: It might be e…

02:09

Determine the derivative.$$f(x)=\frac{e^{2 x^{2}}+1}{x^{2}+1}$$

01:11

02:31

Thorium 234 decays by about $3 \%$ every day. How much of a 10 lb sample rem…

01:12

Evaluate the given definite integral.$\int_{1}^{3} 5 d x$

03:00

Given $P(x)=F(x) S(x),$ where $F$ and $S$ are differentiable functions. Use …