Question

In 1980, the population of a town was 2000 people. The exponential function P(t)=2000(1.05)t models the population of the town since 1980. Which statements are true regarding the population of the town? Select THREE that apply.

A.

The population has increased by 5% each year since 1980.

B.

The population has increased by 105% each year since 1980.

C.

The population has increased by 5 people each year since 1980.

D.

Each year since 1980, the population is 105% of the population of the previous year.

E.

Each year since 1980, the population is 1.05 times the population of the previous year.

Answer 1

Answer:

B. The population has increased by 105% each year since 1980.

D. Each year since 1980, the population is 105% of the population of the previous year.

E. Each year since 1980, the population is 1.05 times the population of the previous year.

Step-by-step explanation:

From the question, we are given the exponential function:

The exponential function P(t)=2000(1.05)^t models the population of the town since 1980.

Exponential growth rate =

P(t) = P(1 + r)^t

Where r = growth rate in percentage

P(t) = Size of the population after t years

t = time in years

Hence,

From the formula above, we can say =

1 + r = 1.05

r = 1.05 - 1

r = 0.05

Converting to percentage = 0.05 × 100 = 5%

1.05 can also converted to percentage and this = 1.05 × 100 = 105 %

The population has increased by 105% each year since 1980.

Hence, Options, B, D and E is correct