462 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 108. World Population Growth Based on data from 2000 to 2018, world population in millions closely fits the exponential function ƒ1x2 = 6103e0.01167x, where x is the number of years since 2000. (Data from U.S. Census Bureau.) (a) The world population was about 7346 million in 2016. How closely does the function approximate this value? (b) Use this model to predict world population in 2020 and 2030 to the nearest million. 109. Deer Population The exponential growth of the deer population in Massachusetts can be approximated using the model ƒ1x2 = 50,00011 + 0.062x, where 50,000 is the initial deer population and 0.06 is the rate of growth. ƒ1x2 is the total population after x years have passed. Find each value to the nearest thousand. (a) Predict the total population after 4 yr. (b) If the initial population was 30,000 and the growth rate was 0.12, how many deer would be present after 3 yr? (c) How many additional deer can we expect in 5 yr if the initial population is 45,000 and the current growth rate is 0.08? 110. Employee Training A person learning certain skills involving repetition tends to learn quickly at first. Then learning tapers off and skill acquisition approaches some upper limit. Suppose the number of symbols per minute that a person using a keyboard can type is given by ƒ1t2 = 250 - 12012.82-0.5t, where t is the number of months the operator has been in training. Find each value to the nearest whole number. (a) ƒ122 (b) ƒ142 (c) ƒ1102 (d) What happens to the number of symbols per minute after several months of training? Use a graphing calculator to find the solution set of each equation. Approximate the solution(s) to the nearest tenth. 111. 5e3x = 75 112. 6-x = 1 - x 113. 3x + 2 = 4x 114. x = 2x 115. A function of the form ƒ1x2 =xr, where r is a constant, is a power function. Discuss the difference between an exponential function and a power function. 116. Concept Check If ƒ1x2 = ax and ƒ132 = 27, determine each function value. (a) ƒ112 (b) ƒ1-12 (c) ƒ122 (d) ƒ102 Concept Check Give an equation of the form ƒ1x2 = ax to define the exponential function whose graph contains the given point. 117. 13, 82 118. 13, 1252 119. 1-3, 642 120. 1-2, 362 Concept Check Use properties of exponents to write each function in the form ƒ1t2 = kat, where k is a constant. (Hint: Recall that ax+y = ax # ay.) 121. ƒ1t2 = 32t+3 122. ƒ1t2 = 23t+2 123. ƒ1t2 = a 1 3b 1-2t 124. ƒ1t2 = a 1 2b 1-2t
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