Question

an exponential function is?

Answer 1

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

$$(x)=Ab^x$$

where $A$ is a real number and $b$ is a positive number not equal to one.

a)

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

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

b)

$$f(x)=3e^{2x}=(3)(e^2)^x$$

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

c)

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

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

d)

$$v(s)=s^x$$

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

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