Question

The population of a city is growing at an uninhibited rate of 1.6% per year. The city's initial population was 125,000. How long will it take the population of that city to reach 175,000? Round to the nearest tenth.
a. 56.5 years
b. 21.0 years
c. 9.1 years
d. 37.8 years

Answer 1

Answer:

B

Step-by-step explanation:

First we find how much of 125000 is increasing. Once we do that, it is basically a slope intercept equation.

We know that 1.6 percent of 125000 is 2000.

We know have y=2000x+125000

There are two ways to solve this, either plug in the given values of a, b, c, and d into the equation and see if it equal 175000, or we we set the equation equal to 175000

If we do the second easiet option, we have

2000x+125000=175000 Use inverse operations

2000x=50000

x=25, or roughly option b.

If we plug in b, we get y=2000(21)+125000 or 167000

Answer 2

21.0 years will it take the population of that city to reach 175,000.

What is population growth rate?

Population growth rate is the change in the number of individuals over a specific period of time. Population growth rate can be interpreted over any time period.

Given

Population of a city is growing at an uninhibited rate of 1.6% per year.

The city's initial population was 125,000.

Based on the given conditions

$125000.(1+0.016)^{x} =175000$

⇒ $125000.(1.016)^{x} =175000$

⇒ $(1.016)^{x} =\frac{175000}{125000}$

⇒ $(1.016)^{x} =\frac{7}{5}$

⇒ $x=log_{1.016} \frac{7}{5}$

⇒ $x=log_{\frac{127}{125} } \frac{7}{5}$

⇒ x = 21.0

21.0 years will it take the population of that city to reach 175,000.

Find out more information about population growth rate here

https://brainly.com/question/23659639

#SPJ3