Question

The function f(t)=3,502.86(1.15)(t−12) models the amount of money in Gavin's investment account after t years. Gavin says this means that the initial amount in the account was $3,502.86. Is he correct? Why or why not?

A.No, because you need to multiply 3,502.86 to find the initial amount.




B.No, because f(0) is not 3,502.86.




C.Yes, because 3,502.86 is multiplied by the exponential term.




D.Yes, because f(0)=3,502.86

Answer 1

Gavin is incorrect; the initial amount in the account is not $3,502.86 because when evaluating the function at t=0, it results in a different value.

Step-by-step explanation:

The student asked if the initial amount in Gavin's investment account was $3,502.86 based on the function f(t) = 3,502.86(1.15)(t−12). Gavin is incorrect. The initial amount is determined by evaluating the function at t = 0. In this case, substituting t with 0 gives
`f(0) = 3,502.86(1.15)^(-0)`, which simplifies to a different amount than $3,502.86, because
`(1.15)^(-0)` is not equal to 1. Therefore, the correct answer is B: No, because f(0) is not 3,502.86.