Question

an initial amount of 2,400 grows at a rate of 12% every month. Write an exponential equation for the amount y after x months

Answer 1

The expression is y(x) = 2400*(1.12)^x

Explanation:

The initial amount is:

y(0) = 2400

After the first month it is:

y(1) = y(0)*(1 + 12/100) = 2400*(1 + 0.12) = 2400*(1.12)

After the second month it is:

y(2) = y(1)*(1.12) = y(0)*(1.12)*(1.12) = y(0)*(1.12)²

After the third month it is:

y(3) = y(2)*(1.12) = y(0)*(1.12)²*(1.12) = y(0)*(1.12)³

After "x" months, we have:

y(x) = y(0)*(1.12)^x

y(x) = 2400*(1.12)^x