Class work: More exponential modeling

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Merilyn Eaton
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1 November 5, 03 Exponential modeling page Class work: More exponential modeling Exponential equation: f(x) = a b x = (starting amount) (multiplier) x Summary: ways to find the multiplier If you re given a percent rate of increase: multiplier = + (the rate written as a decimal). If you re given a percent rate of decrease: multiplier = (the rate written as a decimal). If you re given a fraction rate of increase: multiplier = + fraction. If you re given a fraction rate of decrease: multiplier = fraction. If you re given a number that s used for repeated multiplication, multiplier = that number. (For example, if a problem says that an amount triples every day, then multiplier = 3.) Class Problems:. Find the multiplier for each change described below. If the description of the change is increase by 6%.06 decrease by 6% 0.94 increase by 0% decrease by 0% increase by 7.89% decrease by 7.89% double it quadruple it twenty times as much half as much increase by 4 decrease by 4 increase by 3 decrease by 3 then the multiplier is

2 November 5, 03 Exponential modeling page Try it in reverse. Here you are given various multipliers. Write a description of each change (for example, increase by or decrease by If the description of the change is then the multiplier is For each of these exponential functions, identify the starting amount, identify whether it is a % increase or decrease, and identify the % change. a. y = (.033) x b. y = 400 (0.4) x b. y = 5. () x

3 November 5 or 6, 03 Exponential modeling page 3 Homework Problems:. Suppose that someone puts their favorite photograph on an enlarging photocopier and enlarges it repeatedly (by copying the original, then copying the copy, then copying the copy, and so on). a. Suppose the copier s zoom enlarges the picture by 5%. Starting with a photocopier that s 3 inches tall, fill in this table with how tall it will be after the first few steps of copying. x = number of times copied f(x) = height b. Write a function formula equation relating x and f(x), giving what the height f(x) will be after copying x times. f(x) = c. The process will have to stop when the full height of the photocopier glass is reached. That maximum height is inches. After how many copying steps will this height be reached? Use table on calculator.. A major newspaper had 800,000 subscriptions in the year 000. The number of subscriptions in each year since then is given by the function f(x) = 800,000 (0.94) x, where x stands for the number of years since 000. a. Has the number of subscriptions been increasing or decreasing? Tell how you know. b. What is the rate of increase or decrease for the number of subscriptions, as a percentage?

4 November 5 or 6, 03 Exponential modeling page 4 c. How many subscriptions will there be in the year 006? d. How many years until there are less than 500,000 subscriptions? Use your table on the calculator. 3. Suppose that a city s population is given by the function f(x) = x, where x stands for the number of years since Mayor O Connor took office. a. Is the population increasing or decreasing each year? By what percent? b. Find the population 4 years after Mayor O Connor took office. c. Evaluate f(0), and explain the meaning of the answer in terms of the city s population. d. Using the Table ([nd][graph]) command on your calculator, complete in this input-output table. year x population f(x)

5 November 5 or 6, 03 Exponential modeling page 5 4. A new laptop computer is worth $,00. Each year, the laptop s value decreases by 30%. a. Write a function formula for V(t), the computer s value after t years. b. Evaluate V(3), and explain the meaning of the answer in terms of the laptop. c. Make an input-output table for function V(t) on your calculator. (You don t have to copy it onto your paper.) Use the table to answer the question: After how many years does the value of the laptop fall below $00? 5. A population of 500 elk is released in a wildlife preserve. Each year, the population grows by 6.4%. a. What is the multiplier number for a 6.4% increase? b. Write a function formula for P(t), the elk population after t years. c. After 3 years, how many elk are there? d. Use an input-output table to get the answer to this question: After how many years will the elk population exceed 800 elk?

UNIT 3A. Uses and Abuses of Percentages

UNIT 3A. Uses and Abuses of Percentages UNIT 3A Uses and Abuses of Percentages PERCENTAGES Per Cent.Per 100.divided by 100 Uses symbol % 25% is read 25 per cent and means 25/100 = 0.25 P% = P/100 Examples 40% = 40/100 = 0.40 100% = 100/100=