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

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

Step-by-step 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