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

Step-by-step explanation:

3502.86 is the capital

1.15 is the interest

While (t - 12) tells us about the period of time.

And f (t) is the amount of money in Gavin's investment account after t years

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.