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

QUESTION 1

Let $n$ represent the number of years.

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

$N(n)=8.7\times 10^5(n)$

Therefore after $25$ years,

$N(25)=8.7\times 10^5(25)$

$N(25)=21750000$

In scientific notation,

$N(25)=2.175\times 10^7$

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

$P_0=9.7\times 10^7$

The population  after 25 years

$P(25)=9.7\times 10^7+2.175\times 10^7$

$P(25)=(9.7+2.175)\times 10^7$

$P(25)=(11.875)\times 10^7$

$P(25)=1.1875\times 10^1 \times 10^7$

$P(25)=1.1875\times 10^1 \times 10^7$

$P(25)=1.1875\times 10^8$

Answer 2

Answer:

1. $2.175*10^{7}$

2. $1.1875*10^{8}$

Step-by-step 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 $1.1875\cdot 10^{8}$.