Question

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

Answer 1

Answer:

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

Step-by-step 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 $(0.95)^{x}$