Question

Question: The population of a country is 9.7 x 107, and is increasing by 8.7 x 105 people each year. Show your work for each calculation, and answer in scientific notation: 1. How many new people are added after 25 years? 2. What is the population after 25 years? Type your answer below:

Answer 1

1.
`2.175*10^(7)`

2.
`1.1875*10^(8)`

Explanation:

We are given that population of a country is
`9.7*10^(7)` , and is increasing by
`8.7*10^(5)` people each year.

1. To find number of people added after 25 years we will multiply 25 by
`8.7*10^(5)`.

`(2.5\cdot 10^(1))\cdot (8.7\cdot 10^(5))`

`(2.5\cdot 8.7)\cdot (10^(1+5))`

`(21.75)\cdot (10^(6))=(2.175)\cdot (10^(7))`

Therefore,
`2.175\cdot 10^(7)` will be added after 25 years.

2. To find out population after 25 years we will add population added in 25 years to initial population.

`9.7*10^(7)+2.175\cdot 10^(7)`

`11.875\cdot 10^(7)`

`1.1875\cdot 10^(8)`

Therefore, population after 25 years will be
`1.1875\cdot 10^(8)`.

Answer 2

QUESTION 1

Let
`n` represent the number of years.

Then each year the number of people added is given by the function

`N(n)=8.7* 10^5(n)`

Therefore after
`25` years,

`N(25)=8.7* 10^5(25)`

`N(25)=21750000`

In scientific notation,

`N(25)=2.175* 10^7`

ANSWER TO QUESTION 2

The population after 25 years can be calculated by adding the increment in population to the initial population.

The initial population

`P_0=9.7* 10^7`

The population after 25 years

`P(25)=9.7* 10^7+2.175* 10^7`

`P(25)=(9.7+2.175)* 10^7`

`P(25)=(11.875)* 10^7`

`P(25)=1.1875* 10^1 * 10^7`

`P(25)=1.1875* 10^1 * 10^7`

`P(25)=1.1875* 10^8`