Chapter ISG, Problem 7.2STP

a.

To determine

To write a function

Answer to Problem 7.2STP

  $A=i+\frac{rt}{100}\times i$

Explanation of Solution

Given information:

Population of elk=780

Growth of rate=2.3%

Calculation:

The equation is $A=i+\frac{rt}{100}\times i$

Where $A$ total population after t years, i is the initial population $\frac{r}{100}$ is the growth of population annually.

b.

To determine

Answer to Problem 7.2STP

1000 is the correct answer.

Explanation of Solution

Given information:

  $A=i+\frac{rt}{100}\times i$

t=11 years

Calculation:

Substituting values,

  $A=780+\frac{(2.3)(11)}{100}\times 780$

Solving,

  $A=780+\frac{(2.3)(11)}{10}\times 78$

So,

  $A=780+197.34$

Hence, number of elks are 977.34 $\approx$ 978

For the approximation, 1000 is the correct answer.

c.

To determine

To find how many years it will take to double population.

Answer to Problem 7.2STP

50 years is the correct option

Explanation of Solution

Given information:

Population of elk and rate of growth

Calculation:

  $A=i+\frac{rt}{100}\times i$

As rate of growth is 2.3%

2.3% of 780= $\frac{2.3}{100}\times 780$

Solving,

= $\frac{23}{1000}\times 780$

Hence, $\approx$ 18 are increased every year.

Elk increased in 1 year=18

Elk increased in 10 years=180

Elk increased in 20 years=360

Elk increased in 40 years=720

Elk increased in 50 years=900

Approximately, the years required to double the population is 50 years.