Question

Which of the following functions represent exponential growth? f(x)=.0001(1.77)^x f(x)=2(1.5)^x/2 f(x)=5(0.5)^-x f(t)=5e^-t

Answer 1

Answer:

Hello There. ☆~\《`°---_●£●__---`°》\~☆

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.

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

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

Hope It Helps!~ ♡

ItsNobody~ ☆

Answer 2

The functions that represent exponential growth are choices (A), (B), and (C). The correct option is A, B, and C.

What is exponential growth?

Exponential growth is the process of gradual increase of quantity over time.

An exponential growth function is represented by

$\rm f(x)=a(b)^{x}$,  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.

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

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

Learn more about exponential growth;

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