Math, asked by brendanpowellbmx14, 1 year ago

Which of the following functions represent exponential growth?

a. f(x)=.001(1.77)^x
b. f(x)=2(1.5)^x/2
c. f(x)=5(0.5)^-x
d. f(t)=5e^-t

Answers

Answered by Pitymys
15

An exponential growth function is represented by

f(x)=a(b)^{x},a>0,b>1.

The given functions can be written as,

A)f(x)=.001(1.77)^x,0.001>0,1.77>1

B)f(x)=2(1.5)^{x/2}=2(\sqrt{1.5} )^x,2>0,\sqrt{1.5} >1

C)f(x)=5(0.5)^{-x}=5(2)^x,5>0,2>1

D) f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e<1.

So the function f(t)=5e^{-t}=5(\frac{1}{e} )^x,5>0,1/e<1 violates the conditions for an exponential growth function. It is an exponential decay function.

The correct choices are (A), (B), (C).

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