The table represents an exponential function.x -3 -2 -1 0 11 2 3445 25 125y 500 100 20 4Does the function in the table represent growth or decay?O The function represents exponential decay because the base equalsThe function represents exponential growth because the base equals13O The function represents exponential decay because the base equals 5.O The function represents exponential growth because the base equals 5.

The given tablex-3-2-10123y500100204

Answered: The table represents an exponential…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter7: Polynomial Equations And Factoring

Section: Chapter Questions

Problem 2CA

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A Skydiver If a skydiver jumps from an airplane, his velocity v, in feet per second, starts at 0 and increases towards terminal velocity, an average-sized man has a terminal T of about 176 feet per second. The difference D=Tv is an exponential function of time, a. What is the initial value of D? b. Two second into fall, the velocity is 54.75 feet per seconds. Find an exponential formula for D. c. Find a formula for v. d. Express the velocity 4 seconds into the fall using functional notation, and then calculate that value.
Use a calculator to help solve each problem. Bluegill population A Wisconsin lake is stocked with 10,000 bluegill. The population is expected to grow exponentially according to the model Pt=P02t/2. How many bluegill will be in the lake in 5 years?
The function f(x)=5x is an exponential function with base______; f(2) =_______, f(0) =______, f(2) =_______, and f(6) =_______.
Depreciation A laptop computer that costs $575 new has a book value of $275 after 2 years. (a) Find the linear model V=mt+b. (b) Find the exponential model V=aekt. (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the computer after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.
Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.
4546 Comparing Exponential and Power Functions In these exercises we use a graphing calculator to compare the rates of growth of the graphs of a power function and an exponential function. a Compare the rates of growth of the functions f(x)=2xandg(x)=x5 by drawing the graphs of both functions in the following viewing rectangles. i [0,5]by[0,20] ii [0,25]by[0,107] iii [0,50]by[0,108] b Find the solutions of the equation 2x=x5, rounded to one decimal place.
4546 Comparing Exponential and Power Functions In these exercises we use a graphing calculator to compare the rates of growth of the graphs of a power function and an exponential function. a Compare the rates of growth of the functions f(x)=3xandg(x)=x4 by drawing the graphs of both functions in the following viewing rectangles: i [4,4]by[0,20] ii [0,10]by[0,5000] iii [0,20]by[0,105] b Find the solutions of the equation 3x=x4, rounded to two decimal places.
Growth Rate Versus Weight Ecologists have studied how a populations intrinsic exponential growth rate r is related to the body weight W for herbivorous mammals. In table 5.2, W is the adult weight measured in pounds, and r is growth rate per year. Animal Weight W r Short-tailed vole 0.07 4.56 Norway rat 0.7 3.91 Rue deer 55 0.23 White-tailed deer 165 0.55 American elk 595 0.27 African elephant 8160 0.06 Find a formula that models r as a power function of W, and draw a graph of this function.
Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.

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