Intermediate Algebra (11th edition)

44.The concentration of a drug injected into the bloodstream decreases with time. The
intervals of time Twhen the drug should be administered are given by

where kis a constant determined by the drug in use, is the concentration at which the

drug is harmful, and is the concentration below which the drug is ineffective. (Source:

Horelick, Brindell and Sinan Koont, “Applications of Calculus to Medicine: Prescribing

Safe and Effective Dosage,” UMAP Module 202.) Thus, if , the drug should be

administered every 4 hr. For a certain drug, , , and. How often

should the drug be administered? (Hint:Round down.)

45.The growth of outpatient surgeries as a percent of total surgeries at hospitals is approxi-
mated by

where xis the number of years since 1900. (Source:American Hospital Association.)

(a)What does this function predict for the percent of outpatient surgeries in 1998?

(b)When did outpatient surgeries reach 50%? (Hint:Substitute for y, then write the

equation in exponential form to solve it.)

46.In the central Sierra Nevada of California, the percent of moisture that falls as snow rather
than rain is approximated reasonably well by

where xis the altitude in feet.

(a)What percent of the moisture at 5000 ft falls as snow?

(b)What percent at 7500 ft falls as snow?

47.The cost-benefit equation

describes the approximate tax T, in dollars per ton, that would result in a p% (in decimal

form) reduction in carbon dioxide emissions.

(a)What tax will reduce emissions 25%?

(b)Explain why the equation is not valid for or.

48.The age in years of a female blue whale of length
Lin feet is approximated by

(a)How old is a female blue whale that measures

80 ft?

(b)The equation that defines t has domain

. Explain why.

Use the change-of-base rule ( with either common or natural logarithms) to find each loga-
rithm to four decimal places. See Example 7.

55.logp e 56.logp 10 57.loge 12

log 7 4 log 322 log 6235

log 3 12 log 4 18 log 5 3

246 L 687

t=-2.57 ln a

87 - L

63

b.

p= 0 p= 1

T=-0.642-189 ln 11 - p 2

ƒ 1 x 2 =86.3 ln x-680,

ƒ 1 x 2 =- 1317 +304 ln x,

k= 31 C 2 = 5 C 1 = 2

T= 4

C 1

C 2

T=

1

k

ln

C 2

C 1

,

SECTION 10.5 Common and Natural Logarithms 611