Question

A deposit of $5,000 is made into a savings account that offers 7.5% annual interest. Which equation models the amount of money in the account after t years?

P(t) = 5,000(1.75)t
P(t) = 5,000(1.075)t
P(t) = 5,000(0.925)t
P(t) = 5,000(0.25)t

Answer 1

The correct answer is B, 5,000(1.075)t

Answer 2

Answer:
`P(t)=5,000(1.075)^t`

Explanation:

Given: The initial deposit = $5000

The rate of annual interest = 7.5% = 0.075

We know that the exponential growth equation is given by :-

`f(x)=A(1+r)^x`, where A is the initial amount, r is the rate of interest in x years.

Thus, for the given situation, the equation models the amount of money in the account after t years is given by :-

`P(t)=5,000(1+0.075)^t\\\Rightarrow P(t)=5,000(1.075)^t`