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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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