Chapter 7.7, Problem 41PFA

To determine

To calculate: The exponential function to select the right option.

Answer to Problem 41PFA

A. $y=3{(0.5)}^x$

Explanation of Solution

Given information: There are two points on the graph (0,3) and (2, 0.75).

Formula: $y=a{(b)}^x$ , where ‘ a’ is initial amount and ‘ b’ is decay factor.

Take two points (0, 3) and (2,0.75) and plug them into the equation to find values of ‘ a’ and ‘ b’ .

Plug in (0, 3) for x and y into the equation.

  $3=a{(b)}^0$

Exponent property says $b^0$ is 1

So,

  $a=3$

Plug in this value ‘ a’ into the equation,

  $y=3{(b)}^x$

Using (2, 0.75)

  $0.75=3{(b)}^2$

Divide both sides by 3.

  $0.25=b^2$

Take square root on both sides, b=0.5

Now, plug in these values into equation.

  $y=3{(0.5)}^x$