Chapter 6.1, Problem 48E

To determine

To write: an exponential function that is represented by the table:

x	0	1	2	3
y	-50	-10	-2	-0.4

Answer to Problem 48E

  $y=-50{\left(0.2\right)}^x$

Explanation of Solution

Concept used:

Exponential function:

  $y=a{b}^x$ ….. (1)

Here, the y-values changes by a factor of b as x increases by 1 and the y intercept is a.

Consider the table given below:

  

It can be observed that corresponding to $x=0$ , the value of y is -50. This implies that y-intercept is -50.

Also from the table it can be observed that as x increases by 1 the y-values changes by a factor of 0.2.

So, substituting $a=-50$ and $b=0.2$ in equation (1), the required exponential function is:

  $y=-50{\left(0.2\right)}^x$