Question

The exponential growth model describes the population in Korea, in thousand t years after 1992. Use the model to solve the following:

a. What was the population of Korea in 1992?
b. By what % is the population of Korea increasing each year?
c. What will be the population of Korea in 2012?
d. When will Korea’s population be 80,000?

The population of a city in the year 1998 is 50,000. If the growth rate is 4%, what is the population in the year 2016?

Answer 1

To find the population of Korea in 1992, substitute t = 0 into the exponential growth model. To find the percentage increase, subtract the population at t = 1 from the population at t = 0, and divide the result by the population at t = 0. To find the population in 2012, substitute t = 20 into the growth model. To find when Korea's population will be 80,000, substitute P = 80,000 into the growth model and solve for t.

Step-by-step explanation:

a. To find the population of Korea in 1992, we need to substitute t = 0 into the exponential growth model. Since t represents the number of years after 1992, substituting t = 0 gives us the population at the year 1992.

b. To find the percentage increase, we can subtract the population at t = 1 from the population at t = 0, and then divide the result by the population at t = 0. Multiply this value by 100 to express it as a percentage.

c. To find the population of Korea in 2012, we need to substitute t = 20 into the exponential growth model.

d. To find when Korea's population will be 80,000, we need to substitute P = 80,000 into the exponential growth model and solve for t. This will give us the number of years after 1992 when the population reaches 80,000.