Question

Which of the following functions would not model exponential decay?o A) h (x) 44 0.89O B) j (x) (0.34O C) b(x) 876 (1)o D z(x)- 7 (0.999)4x-2

Answer 1

Hello,
1^x=1
==>b(x)=876 is not a model exponential.

Answer C

Answer 2

`b(x) = 875(1)^x`

Explanation:

An exponential function
`y=ab^x` is called,

(i) Growth function : If 1 < b,

(ii) Decay function : If 0 < b < 1

`h(x) = 44(0.89)^(2x)`

`\implies h(x) = 44(0.89^2)^2 = 44(0.7921)^x`

∵ 0.7921 < 1

Hence, it is a decay function,

`j(x) = (0.34)^(x-3)= (0.34)^(-3) (0.34)^x\implies j(x) =25.44(0.34)^x`

∵ 0.34 < 1

Hence, j(x) is a decay function,

`b(x) = 875(1)^x \implies b(x) =875`

Which is a constant function,

Hence, b(x) is not an exponential decay function.

`z(x) = 7(0.999)^(4x-2)=7(0.999)^(-2) (0.999)^x=7.014(0.999)^x`

∵ 0.999 < 1

Hence, z(x) is a decay function.