Question

Which of the following options results in a graph that shows exponential growth. F(x) = 0.4(3)^x. F(x) = 3(0.5)^x. F(x) = 0.8(0.9)^x. F(x) = 0.9(5)^-x

Answer 1

$f(x)=a^x\\\\if\ a \ \textgreater \ 1\ then\ a\ function\ is\ an\ exponential\ growth\ function$

$f(x)=0.4(3)^x\to a=3 > 1\ OK!\\f(x)=3(0.5)^x\to a=0.5 < 1 :(\\f(x)=0.8(0.9)^x\to a=0.9 < 1 :(\\f(x)=0.9(5)^{-x}=0.9\left(\dfrac{1}{5}\right)^x\to a=\dfrac{1}{5} < 1\ :($

Answer: $f(x)=0.4(3)^x$