Question

The number of new homes, h(n), has increased at the same rate each year, n, since the growth began. The functions below represent the new construction.



b
(
n
)
=
20
(
1.05
)
n



h
(
n
)
=
5
n
+
20



Which statement about the new construction of businesses and homes is true? Choose the TWO correct answers.


The number of new businesses increases by .05% every year.


Every year since the growth began the construction of new businesses will exceed the construction of new homes.


After 5 years the number of new businesses constructed equal the number of new homes constructed.


At the time the growth began, the number of newly constructed businesses and homes were both 20.


Each year there are 5 new homes that are constructed

Answer 1

Correct answers:
- At the time the growth began, the number of newly constructed businesses and homes were both 20.
- Each year there are 5 new homes that are constructed.

Reasoning:
- b(0)=20(1.05)^0=20 and h(0)=5(0)+20=20, so both start at 20.
- h(n)=5n+20 increases by 5 each year (linear growth with slope 5), so the number of new homes increases by 5 per year.

(The business function multiplies by 1.05 each year, so it grows by 5% per year—not 0.05%—and b(n) does not exceed h(n) for every year.)