logarithmic functions word problems

[Guest]

Hi, I am having trouble with figuring out these word problems. If someone could tell me how to do them and the answers, that would be great. Thanks!

1) A person invests $4000 in an account at 5% interest compounded annually. Let V = f(t) represent the value (in dollars) of the account after "t" years or any fraction thereof.

a) The equation for "f" is f(t)=2000 (1.05t).
b) The V-intercept is (0, 2000).

--When will the balance be $3000?


2) The equation f(t)=1.197(1.0163t) models the world population (in billions) at "t" years since 1900.

Year World Population (billions)
1930 2.070
1940 2.295
1950 2.500
1960 3.050
1970 3.700
1980 4.454
1990 5.279
2000 6.080
2002 6.215

--Many experts believe that the world can support about 10 billion
people. Predict when the population will reach 10 billion.


3) The illicit use of methamphetamine has skyrocketed in rural areas. The chemical by-products of creating the drug are a big environmental hazard, and toxic spill cleanup crews are often called in to clean up abandoned meth labs. The table below shows the number of meth labs cleaned by toxic spill crews in Washington State alone.

Year World Population (billions)
1995 42
1996 146
1997 208
1998 350
1999 792
2000 1458

a) Find an equation for "f."
b) Use "f" to predict in which year the number of meth labs cleaned by
toxic spill crews will equal the number of households in Washington.
Assume there are 2.2 million households in Washington.


4) There are 4 million bacteria on a peach at noon on Tuesday. Assume that a bacterium divides into two bacteria every hour, on average. Let f(t) represent the number of bacteria (in millions) on the peach at "t" hours after Tuesday noon.

a) Find an equation for "f."
b) Find f(24).
c) Find f-1(8000).


5) A person drinks a cup of coffee. We assume that the caffeine enters his bloodstream immediately, and that there was no caffeine in his bloodstream prior to drinking the cofee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 100 milligrams of caffeine.

a) Let f(t) represent the number of milligrams of caffeine in the
person's bloodstream at "t" hours after drinking the cup of coffee.
Find an equation for "f."
b) The person drinks the cup of coffee at 8 AM and goes to bed at 11
PM. Use "f" to predict the amount of caffeine in his bloodstream when
he goes to bed.
c) Suppose the person drinks another cup of coffee 24 hours after the
first cup. How much caffeine will be in his bloodstream from these 2
2 cups of coffee just after drinking the second cup? Explain how you
can find this result without using an equation.

 

[stapel]

Counting parts, you have posted eleven questions here, with no work shown. Do you have no idea what they're talking about (in which case, we need to find some online lessons to send you to), or do you have some understanding of the subject (in which case, please reply showing what you have tried and where you are stuck)?

Thank you.

Eliz.

 

[tkhunny]

1) A person invests $4000 in an account at 5% interest compounded annually. Let V = f(t) represent the value (in dollars) of the account after "t" years or any fraction thereof.

a) The equation for "f" is f(t)=2000 (1.05t).
b) The V-intercept is (0, 2000).

--When will the balance be $3000?

You absolutely MUST spend a little more time on your notation and a LOT more time on showing your work. That "1.05t" should be "1.05^t". If you can't find the superscript, you can show it like this, "1.05^t"

Solve 3000 = 2000*1.05^t for t. You will need logarithms.

 

[Guest]

Eliz, where can I find these lessons because I don't understand how to do these problems.

 

[stapel]

Eliz, where can I find these lessons....

How far back do we need to go? Do you know how to solve basic logarithmic and exponential equations, so you only need some word-problem examples? Or do you need to start back with logs and exponential functions? Or with functions, graphing, and solving in general?

(In all cases, a search engine would likely be useful. For instance, you could go to Google and do a search on "solve log equation" [without the quote-marks] and see if you can find anything helpful in the results.)

Thank you.

Eliz.