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

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

Step-by-step explanation:

Given:

The function, f(t) = 3,502.86 × (1.15)× (t−12)

Simple interest, I = (P × R × t)/100

Where,

P = initial sum of money

R = rate

t = time in years

Amount of money after t years, A = I + P

But I = (P × R × T)/100

A = (P × R × T)/100 + P

= P × (1 + 0.01R) × t

Comparing this equation with the equation above,

P = 3,502.86

= initial sum of money.

Gavin is correct.

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