Exponential and Logarithmic Functions

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Applications and Extensions

A Population Model The resident population of the United States in 2014 was 317 million people and was growing at a rate of 0.7% per year. Assuming that this growth rate continues, the model P(t) = 317(1.007)t − 2014 represents the population P (in millions of people) in year t.

a. According to this model, when will the population of the United States be 400 million people?

b. According to this model, when will the population of the United States be 435 million people?

A Population Model The population of the world in 2014 was 7.14 billion people and was growing at a rate of 1.1% per year. Assuming that this growth rate continues, the model P(t) = 7.14(1.011)t − 2014 represents the population P (in billions of people) in year t.

a. According to this model, when will the population of the world be 9 billion people?

b. According to this model, when will the population of the world be 12.5 billion people?

Depreciation The value V of a Chevy Cruze that is t years old can be modeled by V(t) = 18,700(0.84)t.

a. According to the model, when will the car be worth $9000?

b. According to the model, when will the car be worth $6000?

c. According to the model, when will the car be worth $2000?