5. The value of a sculpture is increasing 5% every month. The original value of the

sculpture is $6400. Identify the exponential growth function to model this situation.

Then find the value of the sculpture after 30 months.

The expression that represents the value of the sculpture by month is:

value (n) = value (0) * 1.05^n

And the value after 30 months is:

$27660.431

Step-by-step explanation:

If the value of the sculpture is increasing 5% every month, then initially it's value will be:

value (0) = 6400

After the first month:

value (1) = value (0) * 1.05

After the second month:

value (2) = value (1) * 1.05 = value (0) * 1.05*1.05 = value (0) * (1.05^2)

After the third month:

value (3) = value (2) * 1.05 = value (0) * (1.05^2) * 1.05 = value (0) * (1.05^3)

Therefore the equation that can model this growth is:

value (n) = value (0) * 1.05^n

After 30 months it'll be:

value (30) = 6400*1.05^ (30) = 27660.431