Question

the value of a sculpture n years after it was made is given by this formula value in pounds (£)=400,32n what was the original value of the sculpture and by what percentage does the value increase each year

Answer 1

The original value of the sculpture is equal to £400.

The percentage by which the value increase each year is 32%.

In Mathematics, an equation which can be used to model an exponential growth rate is given by this mathematical equation (formula):

`A(t) = P(1 + r)^(t)`

Where:

• A(t) represents the future value.
• P represents the initial value or y-intercept.
• r represents the rate of change or growth rate.
• T represents the time.

Based on the exponential functions provided above, we can reasonably and logically deduce that the required exponential growth rate function is given by;

Value in pounds (£) =
`400 * 1.32^n`

When n is 0, the original value of the sculpture can be calculated as follows;

Original value in pounds (£) =
`400 * 1.32^0`

Original value in pounds (£) = £400.

For the percentage rate of change, we have;

1 + r = 1.32

r = 1.32 - 1

r = 0.32 × 100

r = 32%.

Complete Question;

The value of a sculpture n years after it was made is given by this formula;

value in pounds (£) =
`400 * 1.32^n`

What was the original value of the sculpture and by what percentage does the value increase each year