Precalculus 2014
59

 PAGE: 22 SET: Exercises PROBLEM: 59

The function is , where is the number of years since .

Rewrite the function as .

Here represents the year and represents the year .

Graph of the function .

(a)

All possible values of is domain of the function.

is the number of years since .

The model only includes the year from to .

The relevant domain is .

Observe the graph :

All possible values of is the range of the function.

Range is .

(b)

Observe the graph: Approximate - intercept is .

Find the - intercept by substituting in .

- intercept is .

The - intercept represents the percent of population change in .

(c)

Zeros of a function is - intercepts.

Observe the graph : - intercept of the function is .

Zero of the function is .

The zero of the function represents the time at which the percent population change was .

(d)

Find the percent of population change in .

represents the year .

Substitute in .

The percent of population in is %.

This value is does not seem realistic because it would mean that the population increased by about  , which does not seem likely in comparison to the population trends from to .

(a) The relevant domain is and range is .

(b) -intercept is and the -intercept represents the percent of population change in .

(c) Zero of the function is and the zero of the function represents the time at which the percent population change was .

(d) The percent of population in is %.

This value is does not seem realistic because it would mean that the population increased by about  , which does not seem likely in comparison to the population trends from to .

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