Chapter 13 and 14 review
1. Mortimer measures the length of the grass on his lawn at the same time every day. The length of the grass on Mortimer’s lawn is a linear-to-linear function of time. Today, it is 3 cm high. Tomorrow it will be 4 cm high. One week from today, it will be 6 cm high.
(a) How high will the grass be 30 days from today?
(b) When will the grass be 5 cm high?
2. Over time, Frank’s accuracy at the game of darts gets better and better. When Frank was 20 years old, he was only 62 percent accurate. When he was 30 years old, he was 85 percent accurate. Assume that his accuracy will always increase, and will approach arbitrarily close to 100 percent if he lives long enough. Suppose Frank’s accuracy percentage is a linear-to-linear function of his age. How old will Frank be when he is 95 percent accurate?
3. The population of tigers in a certain region is always growing, but will never surpass 1200. In 1980, there were 300 tigers. In 1985, there were 320 tigers. Assume that the population of tigers is a linear-to-linear rational function of time. When will there be 350 tigers? Give your answer in years after 1980.
4. Let f(x) be the linear-to-linear rational function with the following properties.
• It has a horizontal asymptote of y = 40.
• Its graph passes through the point (6, 10).
• Its graph passes through the point (20, 18).
Find f(x).
5. The height of a certain tree is a linear to linear rational function of time. In 1970, the tree was 40 feet tall. In 1980, the tree was 50 feet tall. In 2000, the tree was 65 feet tall. When will the tree be 75 feet tall? Give your answer in years after 1970.
KL Book
3.4 problems 23, 25, 27, 29, 33, 35, 41, 46, 50, 52, 54, 56
Chapter 13 and 14 review
1. Mortimer measures the length of the grass on his lawn at the same time every day. The length of the grass on Mortimer’s lawn is a linear-to-linear function of time. Today, it is 3 cm high. Tomorrow it will be 4 cm high. One week from today, it will be 6 cm high.
(a) How high will the grass be 30 days from today?
(b) When will the grass be 5 cm high?
2. Over time, Frank’s accuracy at the game of darts gets better and better. When Frank was 20 years old, he was only 62 percent accurate. When he was 30 years old, he was 85 percent accurate. Assume that his accuracy will always increase, and will approach arbitrarily close to 100 percent if he lives long enough. Suppose Frank’s accuracy percentage is a linear-to-linear function of his age. How old will Frank be when he is 95 percent accurate?
3. The population of tigers in a certain region is always growing, but will never surpass 1200. In 1980, there were 300 tigers. In 1985, there were 320 tigers. Assume that the population of tigers is a linear-to-linear rational function of time. When will there be 350 tigers? Give your answer in years after 1980.
4. Let f(x) be the linear-to-linear rational function with the following properties.
• It has a horizontal asymptote of y = 40.
• Its graph passes through the point (6, 10).
• Its graph passes through the point (20, 18).
Find f(x).
5. The height of a certain tree is a linear to linear rational function of time. In 1970, the tree was 40 feet tall. In 1980, the tree was 50 feet tall. In 2000, the tree was 65 feet tall. When will the tree be 75 feet tall? Give your answer in years after 1970.
KL Book
3.4 problems 23, 25, 27, 29, 33, 35, 41, 46, 50, 52, 54, 56