498 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. 87. p = a + k ln x , for x 88. r = p - k ln t, for t 89. T = T0 + 1T1 - T0210-kt, for t 90. A = Pr 1 - 11 + r2-n , for n 91. I = E R11 - e-Rt/22, for t 92. y = K 1 + ae-bx , for b 93. y = A + B11 - e-Cx2, for x 94. m= 6 - 2.5 log M M0 , for M 95. log A = log B - C log x, for A 96. d = 10 log I I0 , for I 97. A = Pa1 + r nb tn , for t 98. D= 160 + 10 log x, for x To solve each problem, refer to the formulas for compound interest. A =Pa1 + r nb tn and A =Pert 99. Compound Amount If $10,000 is invested in an account at 3% annual interest compounded quarterly, how much will be in the account in 5 yr if no money is withdrawn? 100. Compound Amount If $5000 is invested in an account at 4% annual interest compounded continuously, how much will be in the account in 8 yr if no money is withdrawn? 101. Investment Time Kurt wants to buy a $30,000 truck. He has saved $27,000. Find the number of years (to the nearest tenth) it will take for his $27,000 to grow to $30,000 at 4% interest compounded quarterly. 102. Investment Time Find t, to the nearest hundredth of a year, if $1786 becomes $2063 at 2.6%, with interest compounded monthly. 103. Interest Rate Find the interest rate, to the nearest hundredth of a percent, that will produce $2500, if $2000 is left at interest compounded semiannually for 8.5 yr. 104. Interest Rate At what interest rate, to the nearest hundredth of a percent, will $16,000 grow to $20,000 if invested for 7.25 yr and interest is compounded quarterly? (Modeling) Solve each application. See Example 11. 105. In the central Sierra Nevada (a mountain range in California), the percent of moisture that falls as snow rather than rain is approximated reasonably well by ƒ1x2 = 86.3 ln x - 680, where x is the altitude in feet and ƒ1x2 is the percent of moisture that falls as snow. Find the percent of moisture, to the nearest tenth, that falls as snow at each altitude. (a) 3000 ft (b) 4000 ft (c) 7000 ft 106. Northwest Creations finds that its total sales in dollars, T1x2, from the distribution of x thousand catalogues is approximated by T1x2 = 5000 log1x + 12. Find the total sales, to the nearest dollar, resulting from the distribution of each number of catalogues. (a) 5000 (b) 24,000 (c) 49,000
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