Exercise 46 Page 279

Practice makes perfect

a We want to draw the graph of the exponential function y=15(3)^x, where x is the number of 20-year periods. Let's make a table of values.

x	15(3)^x	y=15(3)^x
0	15(3)^0	15
1	15(3)^1	45
2	15(3)^2	135

Let's now plot and connect the points ( 0, 15), ( 1, 45), and ( 2, 135) with a smooth curve.

The domain of the function is all real numbers greater than or equal to zero. Domain:& x ≥ 0 We see that the y-values are greater than 15. Hence, the range of the function is all real numbers greater than 15. Range:& y≥ 15

b The y-intercept is found when x=0. We have shown that it is equal to 15 in the table in Part A. It represents the initial population of coyotes.

c Since x is the number of 20-year periods, to find the population of coyotes in 40 years we need to substitute 2 for x. There are two 20-year periods in 40 years.

y=15(3)^x

Substitute

x= 2

y=15(3)^2

CalcPow

Calculate power

y=15(9)

Multiply

y=135

There will be 135 coyotes in 40 years.