78 Chapter 2 Linear Equations and Inequalities in One Variable Note: To use a given formula, substitute the known values in place of the appropriate variables to find the unknown value. Objective 3 Examples Use the appropriate formula to find the requested information. 3a. Use the compound interest formula to find the amount of money in an account if $10,000 is invested for 5 yr at 4.5% interest compounded annually. Round to the nearest cent. Solution 3a. A = P (1 + r)t Begin with the appropriate formula. A = 10,000(1 + 0.045)5 Substitute the given values of P, r, and t. A = 10,000(1.045)5 Add inside the parentheses. A ≈ 10,000(1.2461819) Approximate the exponent. A ≈ 12,461.82 Multiply. So, the amount saved in the account would be $12,461.82 if $10,000 is invested for 5 yr at 4.5% interest compounded annually. 3b. Use the compound interest formula to find how much money must be invested at 5% interest compounded annually to have $4000 in an account after 3 yr. Round to the nearest cent. Solution 3b. A = P(1 + r) t Begin with the appropriate formula. 4000 = P(1 + 0.05)3 Substitute the given values of A, r, and t. 4000 = P(1.05)3 Add inside the parentheses. 4000 ≈ P(1.157625) Approximate the exponent. 4000 P(1.157625) ≈ Divide each side by 1.157625. 1.157625 1.157625 3455.35 ≈ P Simplify. So, an investment of $3455.35 will yield $4000 if invested at 5% interest compounded annually for 3 yr. 3c. The temperature of boiling water is 100°C. Use the Celsius-to-Fahrenheit conversion formula to find this temperature in degrees Fahrenheit. Solution 3c. F = 9 5 C +32 Begin with the appropriate formula. F = 9 5 (100) + 32 Substitute the given value of C. F = 180 + 32 Multiply. F = 212 Add. So, the temperature of 100°C is equivalent to 212°F. 3d. Use the Celsius-to-Fahrenheit conversion formula to find the value of C if F = 59°. Solution 3d. F = 9 5 C +32 Begin with the appropriate formula. 59 = 9 5 C + 32 Substitute the given value of F.
hendricks_intermediate_algebra_1e_ch1_3
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