Question

In 2010 the town of Applewood had an estimated population of 22,000 people, and its annual growth rate was estimated to be 1.8%.

The population of Applewood is equal to the function P(n), where P(n) = 22,000(1.018)n, and n is the number of years since 2010.

To better understand the future needs of the town, the town council has graphed P(n).

Determine whether each of the following conclusions are correct conclusions about the graph of P(n). Select Yes or No for each conclusion.
Conclusion Yes No
The population of Applewood, P(n), equals 0 when n = 0.


The behavior of the left end of the graph flattens out indicating that as n approaches negative infinity the population of Applewood approaches 0.


The behavior of the right end of the graph is upward indicating that as n approaches infinity the population of Applewood approaches infinity.

Answer 1

The answer in the procedure

Explanation:

Let

P------> the population of Applewood

n-----> the number of years since 2010

we have

`P(n)=22,000(1.018^(n))`

using a graphing tool

see the attached figure

Verify each conclusion

a) The population of Applewood, P(n), equals 0 when n = 0

The conclusion is No

For n=0

The population is equal to P(0)=22,000 people

b) The behavior of the left end of the graph flattens out indicating that as n approaches negative infinity the population of Applewood approaches 0

The conclusion is Yes

see the graph

c) The behavior of the right end of the graph is upward indicating that as n approaches infinity the population of Applewood approaches infinity

The conclusion is Yes

see the graph