# Analysing a function

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Using the Rational Function Paper (attached), analyze the following the four functions. You may either type your responses or turn in a scanned handwritten document, just don’t forget to provide a sketch of your graph either way! Don’t be ashamed to use a online graphing utility.

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Step 2

“Extension Problems” involving logarithmic and exponential functions. Try all four of these problems below, and then analyze each of the functions. Keep in mind that some of the numbers are rather larger, so when you are sketching the graph it is okay to just provide a “sketch” versus a detailed plot of the points. Just make sure that you accurately depict all of the key components!

1. 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?

2. 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?

3. 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?

4. Depreciation. The value V of a Honda Civic LX that is t years old can be modeled by

V(t) = 18,955(0.905)t.

a. According to the model, when will the car be worth \$16,000?

b. According to the model, when will the car be worth \$10,000?

c. According to the model, when will the car be worth \$7500?

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