Solving Exponential & Solving Exponential & Logarithmic Logarithmic EquationsEquations

Solving Exponential & Solving Exponential & Logarithmic Logarithmic EquationsEquations

Part IIPart II

Big Charlie is determined to win Nathan’s July 4th frankfurter eating contest, so he’s decided to train for it by sitting down once a week and eating franks according the formula where t = 0 is the week of Jan 1.( ) 9(1.0423)tf t

a. How many franks will Big Charlie eat on Jan 1?b. At what rate is he increasing the franks?c. How many franks will he eat during week 10 ?d. If Fat Tony won the contest last year by eating 25 hotdogs, will Big Charlie beat that record on July 4th? (week 26) How many will he consume?

Since January 1980, the population of the city of Brownville has grown according to the mathematical model

y = 720,500(1.022)x, where x is the number of years since January 1980.

a. Explain what the numbers 720,500 and 1.022 represent in this model. b. If this trend continues, use this model to predict the year during which the

population will reach 1,548,800.

Environmentalists have been tracing the reindeer population of Lapland. In 1967, the population was 250 thousand. If the population decreases at an annual rate of 4.86%, present this function as an exponential equation.

A. Determine in what year the reindeer population equals 100 thousand.B. If a population of less than 50 thousand puts the reindeer on the endangered species list, in what year will that happen?

The Abrahams just had a new above ground pool installed in their backyard last month, but then went away for the weekend. On Saturday, the pool developed a leak and water has been leaking out of the pool at the rate of 3% per hour. If the pool originally held 17,420 gallons,a. Write the exponential equation which models this function. b. After how many hours, to the nearest tenth of an hour, will the pool be half-

full?

As cars get older, they are worth less than when they were new. This is called depreciation. Suppose you bought a new 2009 Expedition for $39,389 that depreciates approximately 18% per year. a. Write the equation which models this situation. b. Determine the value of the car after 1 year.

c. When will the car be worth less than

$5000?

The number of milligrams of drug d remaining in a patient’s bloodstream t hours after it has been administered is given by the equation:

0 06510 3 468 .( ) ( . ) td t

.

a. Find the number of milligrams still in the blood 4 hours after admission. b. How long will it take for the amount of the drug in the bloodstream to halve its original dosage?

The first permanent English colony in America was established in Jamestown, Virginia in 1607. From 1620 to 1780, the population of colonial America could be modeled by the equation

( ) 8863(1.04)tP t where t is the # of years since 1620.

Using logarithms, determine in what year the population of colonial America was approximately 345,000?

A 200 sample of carbon-14 decays according to the formula

200(.886)tQ

where Q is the quantity remaining and t is measured in thousands of years .

•Determine how much carbon-14 remains after25 years.

• Determine when, to the nearest year, there is only 25 of carbon-14 left.

g

g

Your third cousin twice removed just won $180 million in the Mega-Million Lottery. After taxes, she gets $83.4 million. If she decides to invest $75

million at 8.2% interest using the formula A = Pert where A = amount, P = initial investment and r = rate of interest, in what year will that money be worth 100 million, if she makes the investment in 2010?

After t minutes, the amount A of a 100 milligram asthma medication in a patient’sbloodstream is given by the formula

for 0< t < 10.

To the nearest tenth of a minute, how long does it take for 50 milligrams of the medication to enter the patient’s bloodstream?

100 100(0.8)tA

4 4

1 1log

2 2log ( 5) (5 1)x x

Using logarithms, solve for x to the nearest ten thousandth:

3log 562x

Solve, using logs: