Answer to Question #244758 in Algebra for Nanah

Question #244758

an exponential function is?


1
Expert's answer
2021-10-01T12:54:54-0400

An exponential function is a function that can be written in the form

(x)=Abx(x)=Ab^x

where AA is a real number and bb is a positive number not equal to one.

a)


g(t)=53t=(5)(3)tg(t)=\sqrt{5\cdot3^t}=(\sqrt{5})(\sqrt{3})^t

The function g(t)g(t) is exponential. A=5,b=3.A=\sqrt{5}, b=\sqrt{3}.


b)


f(x)=3e2x=(3)(e2)xf(x)=3e^{2x}=(3)(e^2)^x

The function f(x)f(x) is exponential. A=3,b=e2.A=3, b=e^2.


c)


u(x)=2x/3=(1)(23)xu(x)=2^{x/3}=(1)(\sqrt[3]{2})^x

The function u(x)u(x) is exponential. A=1,b=23.A=1, b=\sqrt[3]{2}.


d)


v(s)=sxv(s)=s^x

The function v(s)v(s) is not exponential.

If xx is a real number, then the function v(s)v(s) is power.




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