Question

Enter the exponential function using t (for time) as the independent variable to model the situation. Then find the value of the function after the given amount of time. A new savings account is opened with $200 and gains 3.1% yearly for 8 years. The exponential function that models the situation is . After 8 years, the savings account has $ . , , , and .

Answer 1

Answer:

$(a)\ f(8) = 200(1 + 3.1\%)^8$

(b) After 8 years, the savings account has $255.32

Step-by-step explanation:

Given

$a = 200$ ---- initial (i.e. when t = 0)

$r =3.1\%$

$t = 8$

Solving (a): Model the situation

For growth, an exponential function is represented as:

$f(t) = a(1 + r)^t$

This gives:

$f(8) = 200(1 + 3.1\%)^8$

Solving (b): The solution to (a)

We have:

$f(8) = 200(1 + 3.1\%)^8$

Express percentage as decimal

$f(8) = 200(1 + 0.031)^8$

$f(8) = 200(1.031)^8$

$f(8) = 200*1.2766$

$f(8) = 255.32$