In 2000, the population of a state was 6.8 million people and was growing at a rate of about 0.32% per year. At this growth rate, the function f (x) = 6.8 (1.0032) x gives the population, in millions x years after 2000. Using this model, find the year when the population reaches 7 million people. Round your answer to the nearest whole number. The population will reach approximately 7 million people during the year.

Question

Mary Anthony

Mathematics

13 April, 05:06

In 2000, the population of a state was 6.8 million people and was growing at a rate of about 0.32% per year. At this growth rate, the function f (x) = 6.8 (1.0032) x gives the population, in millions x years after 2000. Using this model, find the year when the population reaches 7 million people. Round your answer to the nearest whole number. The population will reach approximately 7 million people during the year.

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Answers (1)

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Amira · Answer 1

9 years. Rounded.

Step-by-step explanation:

Givens

f (x) = 7 (the amount you would like to see reached which is 7 million).

6.8 = Current population.

1.0032 = the base increase.

x = the number of years

Equation

f (x) = Current * Base^x

Solution

7 = 6.8 * (1.0032) ^x Divide both sides by 6.8

7/6.8 = 6.8 * (1.0032) ^x/6.8 Do the division

1.0294 = (1.0032) ^x Take the log of both sides. (You could use ln)

log (1.0294) = x * log (1.0032) Calculate.

0.0126 = x *.001387 Divide by 0.001387

0.0126/0.001387 = x Divide

9.08 years. = x Answer