Question

1. Naya invests $7500 in an account which accrues interest continuously at a rate of 4.5%. Write an exponential growth function to model the value of her investment after ( t ) years.

a. ( V(t) = 7500e^0.045t )
b. ( V(t) = 7500(1 + 0.045)^t )
c. ( V(t) = 7500(1 - 0.045)^t )
d. ( V(t) = 7500e^-0.045t )

2. How much interest does Naya earn in the first six months to the nearest dollar?
a. $169
b. $337
c. $84
d. $421

3. How much money, to the nearest dollar, is in the account after 8 years?
a. $11,310
b. $10,275
c. $12,542
d. $9,687

Answer 1

The exponential growth function to model Naya's investment is V(t) = 7500e^0.045t. Naya earns approximately $169 in the first six months. The amount in the account after 8 years is approximately $12,542.

Step-by-step explanation:

The exponential growth function to model the value of Naya's investment after (t) years is option a. ( V(t) = 7500e^0.045t ).

To find how much interest Naya earns in the first six months, we need to calculate the value of the investment after six months and subtract the initial investment of $7500 from it. Plugging in t = 0.5 into the exponential growth function, we get V(0.5) = 7500e^0.045(0.5) ∼ 7500e^0.0225. Evaluating this expression, Naya earns approximately $169 in the first six months.

To find the amount of money in the account after 8 years, we need to plug in t = 8 into the exponential growth function. V(8) = 7500e^0.045(8) ∼ 7500e^0.36. Evaluating this expression, Naya will have approximately $12,542 in the account after 8 years. Therefore, the correct answer to question 3 is option c. $12,542.