Comparing Linear and Exponential Models Exercises

Subsection 2.3 Comparing Linear and Exponential Models Exercises

Refer to the population of Las Vegas, NV, for given years as shown in Table 2.3.15.
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Table 2.3.15. Population, $P(t)\text{,}$ of Las Vegas $t$ years after 1980
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$t$ 0 10 20 30

$P(t)$ 164,674 259,834 484,487 583,756
1. Using the population of Las Vegas in 1980 and 2010, build an exponential model for $P(t)\text{.}$
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2. Use your exponential model to predict the population of Las Vegas in 1990. How does your prediction compare with the actual population at that time?
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3. Use your exponential model to predict in what year the population of Las Vegas will be 600,000.
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4. Using the population of Las Vegas in 1980 and 2010, build a linear model for $P(t)\text{.}$
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5. Do you think the linear model or the exponential model is a better fit to the data? Explain.
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6. What could happen in the future that would make the model fail?
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The town of Allen had a population of 36,000 in 1980, and has been growing at 2.2% per year. The town of Berry had a population of 44,200 in 1980, and a population of 48,000 in 1990.
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1. Find an exponential model, $A(t)\text{,}$ for the population of Allen $t$ years after 1980.
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2. Find an exponential model, $B(t)\text{,}$ for the population of Berry $t$ years after 1980.
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3. When did the population of Allen reach 45,000?
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4. When did the population of Allen equal the population of Berry?
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5. What is the average number of people added to Allen between 1980 and 2000?
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The owners of a movie theater know that the number of people who attend is a function of the price of the tickets. The theater has a capacity of 240 people. If tickets are sold for $1, the theater will fill up completely. On the other hand, if the theater charges $21/ticket, no one will buy tickets.
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1. Assuming that the number of tickets sold, $S(t)$ is a linear function of the price, $t\text{,}$ write an equation for $S(t)\text{.}$
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2. At what price will the theater fill 150 seats?
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A baseball is launched into the air from a height of $2$ meters and with an initial upward velocity of $25$ meters/second. The ball’s height above ground is given by the equation $H(t)=-4.9t^2 + vt + h\text{,}$ where $H$ is in meters and $t$ is in seconds.
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1. Write an equation to model the height of a ball.
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2. How long is the ball in the air?
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3. What is the maximum height reached by the ball?
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4. On what interval is the height of the ball increasing?
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\(t\)	0	10	20	30
\(P(t)\)	164,674	259,834	484,487	583,756

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