Name: ______________________________ Date: _______________________________ Exponential Growth
Homework 1. Ray is a contestant on a quiz show. Every time he answers a question correctly, his winnings double. If he answers the first question correctly his winnings are $1,000; if he answers the second question correctly, his winnings increase to $2,000 and so on. a. Complete the table to show Ray’s winnings after each correct answer. Correct Answers 1 2 3 4 5 6 7
Winnings ($)
b. On the grid, graph the (Correct Answers, Winnings) data from the table.
Domain:
Range:
c. Write an equation for the relationship between the number of correct answers, c, and the winnings, w.
d. How many questions must Ray answer correctly to win at least $1,000,000?
2. On the first day of school, you notice a few patches of fungus on the leaves of the pumpkin vines in your garden. You estimate the area covered by the fungus and find that the patches cover about 1 cm2. Suppose that the leaf area covered by this kind of fungus changes as graphed below.
Area of Fungus (sq. cm)
Pumpkin Leaves 68 64 60 56 52 48 44 40 36 32 28 24 20 16 12 8 4 0 0
1
2
3
4
Day
a. Complete the table to show what will happen to the fungus on the leaves during the first week of school. Day 0
1 2 3 4 5
Area of fungus (cm2) 1
b. What type of relationship does the fungus situation represent (linear, quadratic or exponential)? How do you know? (explain in complete sentences).
c. Write an equation for the fungus area, A, after d days.
d. How much area will the fungus cover after 8 days?
Explain how you found your answer.
e. After how many days will the fungus cover at least 1 million cm2 ?
3. Study the pattern in each table below. Tell whether the relationship between x and y is linear, exponential, or neither, then write the equation if it is linear or exponential a. Type of relationship: _____________________
x y
1 9
2 16
3 23
Equation: _____________________
4 30
5 37
b. Type of relationship: _____________________
x y
1 20
2 100
3 500
c. Type of relationship: _____________________
x y
0 1 16
1 1 4
0 500
1 435
2 370
e. Type of relationship: _____________________
x y
1 600
2 300
4 2500
3 200
3 4
b. 2 x 6 c. 2 + 2 + 2 + 2 + 2 + 2 d. 2 + 6
4 16
5 64
Equation: _____________________
3 305
4 240
5 175
Equation: _____________________
4 150
4. Which of these is another way to write 26 ? (4 points) a. 2 x 2 x 2 x 2 x 2 x 2
5 12,500
Equation: _____________________
2 1
d. Type of relationship: _____________________
x y
Equation: _____________________
5 120
5. Which of the following is written in scientific notation? (4 points) a. 30.2 x 103 b. 5.22 x 112 c. 1.12 + 107 d. 4.18 x 106 6. In the following exponential growth situations, determine the growth factor and yintercept. a.
y = 9(3)x
growth factor = ______
y-intercept = ______
b. The population of mice in Mrs. Fiebelkorn’s classroom triples each month. After one month she has 18 mice, after two months she has 54 mice, after three months she has 162, etc. growth factor = ______
y-intercept = ______
