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45–46 ■ 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
(i)
(ii)
(iii)
(b) Find the solutions of the equation
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Chapter 4 Solutions
EBK ALGEBRA AND TRIGONOMETRY
- Decrease in Bacteria When an antibiotic is introduced into a culture of 50,000 bacteria, the number of bacteria decreases exponentially. After 9 hours, there are only 20,000 bacteria. Write an exponential equation to express the growth function y in terms of time t in hours. In how many hours will half the number of bacteria remain?arrow_forwardThe function f(x)=5x is an exponential function with base______; f(2) =_______, f(0) =______, f(2) =_______, and f(6) =_______.arrow_forwardTracer Dye The amount of a tracer dye injected into the blood stream decrease exponentially, with a decay constant of 3 per minute. If 6 cc are present initially, how many cubic centimeters are present after 10 minutes? Here k will be negative.arrow_forward
- Maria, a biologist is observing the growth pattern of a virus. She starts with 100 of the virus that grows at a rate of 10% per hour. She will check on the virus in 24 hours. How many viruses will she find?arrow_forwardMatch the exponential function with one of the graphs labeled I,II,III and IV, shown below. (a) f(x)=2x (b) f(x)=2x (c) f(x)=2x (d) f(x)=2xarrow_forwardGrowth 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.arrow_forward
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