The V(t)=1.50(1.17)^t represents the value V (t), in dollars, of a comic book t years after its purchase in 2000. Determine the annual growth rate in the value of the comic book and its value in 2025.

We will see that the annual growth rate is of 17%, and in the year 2025, the value will be $75.99.

Exponential growth functions:

A general exponential growth can be written as:

f(x) = A*(1 + r)^x

Where A is the initial value and r is the growth rate. Now we can rewrite our function to get:

V(t) = 1.50*(1 + 0.17)^t

Then you can see that the growth rate is 0.17, or 17% in percentage form (to get it just multiply it bt 100%).

To get the value of the comic book in 2025 you just need to evaluate the function in t = 25 (25 years after the 2000).

V(25) = 1.50*(1 + 0.17)^25 = 75.99

So the value in 2025 is $75.99

If you want to learn more about exponential equations, you can read:

link

Growth rate is 17%

2025 value is $76

Step-by-step explanation:

Here, we want to determine the annual growth rate

The general equation form is;

F = l( 1 + r)^n

where F is the future value

I is the initial value

r is the growth rate

n is the numbering years

To get the growth rate, we simply equate what we have in the bracket to 1 + r

Thus;

1 + r = 1.17

r = 1.17-1

r = 0.17

0.17 is same as 17/100 which is same as 17%

Secondly, we want to get the value of the book in 2025

What we have to do here is to substitute (2025-2000) for t which is 25

We have;

V(t) = 1.50(1.17)^25

V(25) = 75.986 which is approximately 76