Which of the following options results in a graph that shows exponential growth?

Asked by maham237 @ 27/11/2020 in Mathematics viewed by 349 People

a. f(x) = 0.4(3)x
b. f(x) = 3(0.5)x
c. f(x) = 0.8(0.9)x
d. f(x) = 0.9(5)−x

Answered by maham237 @ 27/11/2020

A function $f(x)=b\cdot a^x$ shows

exponential growth, if $a>1;$
exponential decay, if $0$

Consider all options:

A. The function $f(x)=0.4\cdot 3^x$ shows exponential growth, because $3>1.$

B. The function $f(x)=3\cdot 0.5^x$ shows exponential decay, because $0$

C. The function $f(x)=0.8\cdot 0.9^x$ shows exponential decay, because $0$

D. The function $f(x)=0.9\cdot 5^{-x}=0.9\cdot \left(\dfrac{1}{5}\right)^x$ shows exponential decay, because $0$

Answer: correct choice is A

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