Chapter 7.7, Problem 38PFA

To determine

We have to determine an equation from four alternatives through which the two points (0, 2) and (2, 12.5) passes.

Answer to Problem 38PFA

The correct option is (A) $y=2{(2.5)}^x$

Explanation of Solution

The given points are (0,2) and (2,12.5) , if we place value of x-coordinate and y-coordinate in the equation $y=2{(2.5)}^x$

Then, for

  $\begin{array}{l}x=0,\text{ y=2(2}{\text{.5)}}^0\\ \text{ =2}\times \text{1=2}\end{array}$

And for

  $\begin{array}{l}x=2,\text{ y=2(2}{\text{.5)}}^2\\ \text{ =2}\times 2.5\times 2.5\\ \text{ =5}\times \text{2}\text{.5=12}\text{.5}\end{array}$

Thus the points (0, 2) and (2, 12.5) satisfies the equation $y=2{(2.5)}^x$ .

So the correct option is “A”