Chapter 7, Problem 64SGR

To determine

To calculate: The exponential function that passes through the two points $\left(2,20\right)$ and $\left(4,80\right)$ .

Answer to Problem 64SGR

The exponential function passes through the points $\left(2,20\right)$ and $\left(4,80\right)$ is $y=5{(\pm 2)}^x$

Explanation of Solution

Given information: The two points $\left(2,20\right)$ and $\left(4,80\right)$ .

Calculation:

Assume exponential function is $y=a{(b)}^x$

Put x = 2 and y = 20 in above equation

  $20=a{(b)}^2$

  $20=a{b}^2$  …(i)

Put x = 4 and y = 80 in above equation

  $80=a{(b)}^4$

  $80=a{b}^4$  …(ii)

Now from (i) and (ii) one can get

  $\frac{80}{20}=\frac{a{b}^4}{a{b}^2}$

4 = b²

  $b=\pm 2$

Use value of b in (i) to get a =5

Thus, the exponential function is $y=5{(\pm 2)}^x$

Conclusion:

The exponential function passes through the points $\left(2,20\right)$ and $\left(4,80\right)$

is $y=5{(\pm 2)}^x$