Question

The equation y = 3000(1 + 0.03)^n is used to model the amount of money, y, in dollars, in a savings account after n years.

How would the equation be written if the interest rate had been 4% per year?

A. y = 3000(1 + 0.03)^4

B. y = 3000(4 + 0.03)^n

C. y = 3000(1 + 0.04)^n

D. y = 3000(1 + 0.04)^4

Answer 1

The correct option is C.

Explanation:

The given equation is

`y=3000(1+0.03)^n`

Where, y is the amount of money in dollars and n is number of years.

It is an exponential growth model. The standard form of this model is

`y=P_0(1+r)^t`

Where, P₀ is initial amount, r is rate and t is time.

So according to the given equation initial amount of money is 3000, growth rate is 0.03 and time is n years.

If the growth rate is 4% or 0.04, then the model can be written as

`y=3000(1+0.04)^n`

Therefore option C is correct.