graph the exponential function.\n\n$f(x)=\\frac{5}{2}(2)^{x}$\n\nplot five points on the graph of the…

Explanation:

Step1: Substitute (x = - 2)

$$ \begin{align*} f(-2)&=\frac{5}{2}(2)^{-2}\ &=\frac{5}{2}\times\frac{1}{4}\ &=\frac{5}{8} = 0.625 \end{align*} $$ The point is ((-2,0.625))

Step2: Substitute (x=-1)

$$ \begin{align*} f(-1)&=\frac{5}{2}(2)^{-1}\ &=\frac{5}{2}\times\frac{1}{2}\ &=\frac{5}{4}=1.25 \end{align*} $$ The point is ((-1,1.25))

Step3: Substitute (x = 0)

$$ \begin{align*} f(0)&=\frac{5}{2}(2)^{0}\ &=\frac{5}{2}\times1\ &=\frac{5}{2} = 2.5 \end{align*} $$ The point is ((0,2.5))

Step4: Substitute (x = 1)

$$ \begin{align*} f(1)&=\frac{5}{2}(2)^{1}\ &=\frac{5}{2}\times2\ &=5 \end{align*} $$ The point is ((1,5))

Step5: Substitute (x = 2)

$$ \begin{align*} f(2)&=\frac{5}{2}(2)^{2}\ &=\frac{5}{2}\times4\ &=10 \end{align*} $$ The point is ((2,10))

Answer:

The five points are ((-2,0.625)), ((-1,1.25)), ((0,2.5)), ((1,5)), ((2,10))