Question

1. From 2010-2020 the median home value in the city of Fort William grew exponentially. The median home value during this time period changed by 12% per year.

1. If the 1-year percent change is 12%, what is the 1-year growth factor?

2. Use your answer to part (a) to complete the following table of values showing the median home value in Fort William at various times.

   years since the beginning of 2010, tt	median home value in Fort William (in dollars)
   0	182,400
   1	204,288
   2
   3.25	263,623
   4.25
   5.25

3. Define a function ff that models the median home value in Fort William tt years since the beginning of 2010 (assuming 0≤t≤10). Be sure to use function notation.

2.    A city's population grows exponentially by 5% per year.

1. What is the 1-year growth factor for the population?

2. Fill in the missing information in the table below.

   years since the beginning of 2015, n	the city's population, p=g(n)
   0	160,000
   1	168,000
   2	176400
   4.25	196,800
   5.25	206711

c. Define a function g to model the citys population n years since the beginning of 2015.

3. The given table of values represents an exponential function (that is, a relationship where the growth factor is constant for the same size changes in x).

x	y=f(x)
-1	384
0	576
1	864
2	1,296

1. Use the entries in the table to determine the 1-unit growth factor for y in this relationship.

   The 1-unit growth factor is .

2. The 1-unit percent change for values of y is %

3. Define a formula for function f. Be sure to use function notation.

4. Fill in the missing entries in the table. Note: Pay close attention to how the values of x change. Not all changes are 1 unit. You can also use the formula you defined.

x	y=f(x)
-1	384
0	576
1	864
2	1,296
3
5
	14,762.25

Answer 1