for the function f(x)=10e^x, calculate the following function values. give an exact answer or an answer to…

Explanation:

Step1: Substitute $x = - 3$

Substitute $x=-3$ into $f(x)=10e^{x}$, we get $f(-3)=10e^{-3}=10\times\frac{1}{e^{3}}$. Since $e\approx2.71828$, $f(-3)=10\times\frac{1}{(2.71828)^{3}}\approx10\times\frac{1}{20.08554}\approx0.498$.

Step2: Substitute $x = - 1$

Substitute $x = - 1$ into $f(x)=10e^{x}$, we get $f(-1)=10e^{-1}=10\times\frac{1}{e}\approx10\times\frac{1}{2.71828}\approx3.679$.

Step3: Substitute $x = 0$

Substitute $x = 0$ into $f(x)=10e^{x}$, we know that $e^{0}=1$, so $f(0)=10\times e^{0}=10\times1 = 10$.

Step4: Substitute $x = 1$

Substitute $x = 1$ into $f(x)=10e^{x}$, we get $f(1)=10e^{1}\approx10\times2.71828 = 27.183$.

Step5: Substitute $x = 3$

Substitute $x = 3$ into $f(x)=10e^{x}$, we get $f(3)=10e^{3}\approx10\times20.08554=200.855$.

Answer:

$f(-3)\approx0.498$ $f(-1)\approx3.679$ $f(0)=10$ $f(1)\approx27.183$ $f(3)\approx200.855$