# Exponential and Logarithmic Functions

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The exponential models describe the population of the indicated country, A, in millions, t years after 2003. Use these models to solve 2,4 and 6.

India A = 1049.7e^0.015t

Iraq A = 24.7e^0.028t

Japan A = 127.2e^0.001t

Russia A = 144.5e^- O.004t

2. What was the population of Iraq in 2003?

4. Which country has a decreasing population? By what

percentage is the population of that country decreasing

each year?

6. When will India's population be 1416 million?

About the size of New Jersey, Israel has seen its population soar to

more than 6 million since it was established. With the help of US.

aid, the country now has a diversified economy rivaling those of

other developed Western nations. By contrast, the Palestinians, living

under Israeli occupation and a corrupt regime, endure bleak condi-

tions. The graphs show that by 2050, Palestinians in the West Bank,

Gaza Strip, and East Jerusalem will outnumber Israelis. Exercises

7?8, involve the projected growth of these two populations.

*SEE ATTACHMENT FOR GRAPH*

8. a. In 2000, the population of the Palestinians in the West

Bank, Gaza Strip, and East Jerusalem was approximately

3.2 million and by 2050 it is projected to grow to 12 mil-

lion. Use the exponential growth model A = A0ekt, in

which t is the number of years after 2000, to find the expo-

nential growth function that models the data.

b. In which year will the Palestinian population be 9 million?

An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e ^-0.000121t describes the amount of carbon-14 present after t years. Use this model to solve 10.

10. How many grams of carbon-14 will be present in 11,430 years?

12. The half-life of the radioactive element plutonium-239 is

25,000 years. If 16 grams of plutonium-239 are initially

present, how many grams are present after 25,000 years?

50,000 years? 75,000 years? 100,000 years? 125,000 years?

Use the exponential decay mode/for carbon-14, A = A 0 e^ -0.000121t

to solve Exercises 13?14.

14. Skeletons were found at a construction site in San Francisco

in 1989. The skeletons contained 88% of the expected

amount of carbon-14 found in a living person. In 1989 how

old were the skeletons?

16. A bird species in danger of extinction has a population that is

decreasing exponentially (A = Aoekt). Five years ago the

population was at 1400 and today only 1000 of the birds are

alive. Once the population drops below 100, the situation will

be irreversible. When will this happen?

18. Use the exponential growth model, A = Aoekt, to show that

the time it takes a population to triple (to grow from A= Aoe^kt) is given by t = In 3

k

Use the formula t = In 2 that gives the time for a population with

k

a growth rate k to double to solve Exercises 19?20. Express each

answer to the nearest whole year.

20. The growth model A = lO4.9e^0.017t describes Mexico's population, A, in millions, t years after 2003.

a. What is Mexico's growth rate?

b. How long will it take Mexico to double its population?

#### Solution Summary

Exponential and Logarithmic Functions are addressed.