1. explain why its exponential and not linear
The growth each year is calculated on the population of the preceding year. Thus, the base number is getting bigger every year, so the year-to-year increase keeps getting larger. It is not a constant slope, as peer the following answer.
2. write an equation to represent the exponential function
Population in year x, Pop(x), where x is 0 for the current (or base) year, when the population is 523,738.
Pop(x) = (523738)*(1+.0251)^x
For year 0, Pop = 523738
Year 3 = (523738)*(1.0251)^3 = 564174
It can be said that this number is being “compounded annually.”
3. create a table to represent the exponential function.
| Year | Population |
| 0 | 523738 |
| 1 | 536884 |
| 2 | 550360 |
| 3 | 564174 |
| 4 | 578334 |
| 5 | 592851 |
| 6 | 607731 |
| 7 | 622985 |
| 8 | 638622 |
| 9 | 654652 |
| 10 | 671083 |
| 11 | 687927 |
a. identify the growth rate in your table: 2.51% per year
b. explain how the growth rate represents an exponential function: A number is being raised to the 1.0251^x power.
4.create a graph to represent the exponential function : Plot the population on the y axis and year on the x.
5.use color to connect and identify “a” and “b” in the table, equation, and scenario
6.identify the following:
a.independent variable Year
b. dependent variable Population
c. domain: For years 0 and above.
d. range: 523738 and above
e. starting point: Year 0
f. growth rate: 0.051 or 2.51%
I hope this helps,
Bob
