Question

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.

Answer 1

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

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