Chapter 7, Problem 63SGR

To determine

To calculate: The exponential function that passes through the points (1, 12) and (2, 36).

Answer to Problem 63SGR

The exponential function passes through the points (1, 12) and (2, 36) is $y=4{(3)}^x$ .

Explanation of Solution

Given information:

The given two points are (1, 12) and (2, 36).

Calculation:

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

Put x = 1 and y =12

  $12=a{(b)}^1$

  $12=ab$ ..........................(i)

Put x = 2 and y = 36

  $36=a{(b)}^2$

  $36=a{b}^2$ ..........................(ii)

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

  $\frac{36}{12}=\frac{a{b}^2}{ab}$

⇒ b =3

Now use value of b in (ii) to obtain a =4

Thus, the exponential function is $y=4{(3)}^x$ .