Question

Which function represents exponential decay with 5% as the rate of decrease?

Answer 1

The function that represents exponential decay is y = 50
`(0.95)^(x)` ⇒ B

Explanation:

The form of the exponential growth function is y = a
`(1+r)^(x)`

The form of the exponential decay function is y = a
`(1-r)^(x)`

• a is the initial value

• r is the rate of increase or decrease in decimal

∵ The function represents exponential decay with 5%

→ By using the second rule above

∴ y = a
`(1-r)^(x)`

∵ The rate of decrease is 5%

∴ r = 5%

→ Change it to decimal by dividing it by 100

∵ 5% = 5 ÷ 100 = 0.05

∴ r = 0.05

→ Substitute it in the equation

∵ y = a
`(1-0.05)^(x)`

∴ y = a
`(0.95)^(x)`

→ Look at the answer to find which equation is written in this form

∴ y = 50
`(0.95)^(x)`

∴ The function that represents exponential decay is y = 50
`(0.95)^(x)`