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A sum of $\$ 5000$ is deposited into an investment account that earns interest at a rate of $9 \%$ per year compounded monthly.a) Write the function $A(t)$ that computes the value of the investment after $t$ years.b) Use your GDC to sketch a graph of $A(t)$ with values of $t$ on the horizontal axis ranging from $t=0$ years to $t=25$ years.c) Use the graph on your GDC to determine the minimum number of years (to the nearest whole year) for this investment to have a value greater than $\$ 20000$.

Algebra

Chapter 5

Exponential and Logarithmic Functions

Section 1

Exponential functions

McMaster University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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01:43

A sum of $\$ 5000$ is inve…

04:43

You have $\$ 10,000$ to in…

07:48

(a) If $\$ 1000$ is borrow…

06:18

If money is invested at a …

04:46

Use the table feature of y…

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Suppose $\$ 600$ is deposi…

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Al $12 \%$ compounded annu…

04:58

(a) If 3000 is invested al…

17:54

The formula $t=\frac{\log …

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this problem. We want to come up with the ah function A of t that calculates the compound interest. So, uh, using the same kind of ideas before, instead of calling f ve, we're gonna call it a of T. That is the function notation for thea amount of interest in the amount of investment in the account. This is equal to a national value of 5000 times one plus. The rate being told is nine over 100 times ah k, which is the number of compound ng periods for a year. That's 12 because it's calm pounded monthly. So the power of 12 t and ah, we can simplify that to 5000 times. Ah, nine divided by 1200 plus one would be 1.75 to the power of 12 teeth in part B. We want a graph this ah, this equation dysfunction and then use that function to ah do a cup to do ah estimation for part c So part b, every graft it I'm just comping pace that here This is the function for part B. We were being told to graph this from 0 to 25 on the X axis. So the red curve is thief function A of t and part. See, ah is asking us to use this graph to determine the minimum number of years for this investment to have a value greater than 20,000. So, you see this blue line here? This is Ah, $20,000 mark and it takes us 15.461 years to get to 20,000. Um, the answer wants us or the question wants us to find the minimum number of whole years, so ah, 15 years is not going to cut. It won't get us 20,000. We're gonna have to go to 16 years. We gotta round up in this case 16 years. Will, ah allow us to exceed ah investment value of 20,000.

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