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

Which Function Represents Exponential Decay With 5 As The Rate Of Decrease class=

Sagot :

Ashraf82

Answer:

The function that represents exponential decay is y = 50 [tex](0.95)^{x}[/tex] ⇒ B

Step-by-step explanation:

The form of the exponential growth function is y = a [tex](1+r)^{x}[/tex]

The form of the exponential decay function is y = a [tex](1-r)^{x}[/tex]

  • 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 [tex](1-r)^{x}[/tex]

∵ 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 [tex](1-0.05)^{x}[/tex]

∴ y = a [tex](0.95)^{x}[/tex]

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

∴ y = 50 [tex](0.95)^{x}[/tex]

∴ The function that represents exponential decay is y = 50 [tex](0.95)^{x}[/tex]

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