Intermediate Algebra (11th edition)

10.6 Solve each equation. Give solutions to three decimal places.

42. 43. 44.

Solve each equation. Give exact solutions.

51.Concept Check Consider the following “solution” of the equation WHAT
WENT WRONG?Give the correct solution set.

Original equation

Power rule for logarithms

Divide each side by 2.

Write in exponential form.

Solution set:

Solve each problem. Use a calculator as necessary.

52.If $20,000 is deposited at 4% annual interest compounded quarterly, how much will be in
the account after 5 yr, assuming no withdrawals are made?

53.How much will $10,000 compounded continuously at 3.75% annual interest amount to in
3 yr?

54.Which is a better plan?

Plan A: Invest $1000 at 4% compounded quarterly for 3 yr

Plan B: Invest $1000 at 3.9% compounded monthly for 3 yr

55.What is the half-life of a radioactive substance that decays according to the function

, where tis in days?

56.A machine purchased for business use depreciates,or loses value, over a period of years.
The value of the machine at the end of its useful life is called its scrap value.By one
method of depreciation (where it is assumed a constant percentage of the value depreci-
ates annually), the scrap value, S, is given by

where Cis the original cost, nis the useful life in years, and ris the constant percent of

depreciation.

(a)Find the scrap value of a machine costing $30,000, having a useful life of 12 yr and

a constant annual rate of depreciation of 15%.

(b) A machine has a “half-life” of 6 yr. Find the constant annual rate of depreciation.

57.Recall from Exercise 43in Section 10.5that the number of years, , since two
independently evolving languages split off from a common ancestral language is approx-
imated by

where ris the percent of words from the ancestral language common to both languages

now. Find rif the split occurred 2000 yr ago.

58.Concept Check Which one is nota representation of the solution of?

A. B. C.log 7 23 D.log 23 7

ln 23

ln 7

log 23

log 7

7 x= 23

N 1 r 2 =-5000 ln r,

N 1 r 2

S=C 11 - r 2 n,

Q(t)=A 0 e-0.05t

5106

x= 10 101 = 10

x= 101

log x= 1

2 log x= 2

log x^2 = 2

log x^2 =2.

log 4 x+log 4 18 - x 2 = 2 log 2 x+log 2 1 x+ 152 =log 2 16

log 3 1 x+ 22 - log 3 x=log 3 2 log 12 x+ 32 = 1 +log x

log 3 19 x+ 82 = 2 log 5 1 x+ 623 = 2

3 x=9.42 2 x-^1 = 15 e0.06x= 3

CHAPTER 10 Review Exercises 629