[thumper99]

I NEED HELP WITH THE FOLLOWING QUESTIONS:

1. The function F(x)=1+1.6 ln(x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many days of practice can the basketball player make an average of 10 consecutive free throws?

2. Cindy will require $12,000 in 4 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 11% compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.)

3. The logistic growth function f(t)= 20,000/1+332.3e-1.9t models the number of people who have become ill with a particular infection t weeks after its initial outbreak in a particular community. How many people were ill after 9 weeks?

4. The half-life of silicon-32 is 710 years. If 20 grams is present now, how much will be present in 800 years? (Round answer to three decimal places.)

5. The function A=A0e-0.00693x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 300 pounds of the material are placed in the vault, how much time will need to pass for only 80 pounds to remain?

[ebaines]

You shouldn't simply copy your homework assignment and expect us to do it for you. Try to solve these on your own, and tell us what you think the answer is, or if you can't get that far tell us where you got stiuck. Then someone will help you out.

[thumper99]

I do not know where to begin. Can you give me a little jump start then?

[ebaines]

I'll give you a jump start for the first few problems - post back to show us your progress and then we'll work the others.

For problem 1, simply set f(x) = 10 and solve for x. So:

10 = 1 + 1.6 ln(x+1).

Can you take it from there?

For 2, the future value of x dollars compounded at 1% interest for 4 years is
x*1.11^4. Set that equal to $12000 and solve for x.

For 3, just put the value 9 in for t, and see what you get.

[livingthedream]

I have the same questions with different values- I'm having issues on it too

[thumper99]

This is what I did so far:
1. f(10)=1+1.6ln(10+1)
1+1.6ln(11)
4.8366

2. Im stuck on this one:
12,000=x(1.0275)/\4t

3. 20,000/1+332.3e/\-1.9(9)
=19,999

[thumper99]

What did you do so far... lets see if we can help each other

[livingthedream]

well I did the logistic growth function about ill people.

my numbers were f(t)=41,000/1+584.7e-1.3(t) and t=10 weeks.
all I did was plug in and plug into the calculator and got 40,946

[livingthedream]

for the free throws I got to ln^-1*(3.33)=x+1
my original was 1+1.5ln(x+1) and 6 consecutive
my calc doesn't have negative natural logarythem

[thumper99]

I really don't know how you got any of those answers, but I'm just plugging in my numbers too. How did you get that for the logistic growth one?

[livingthedream]

Calculator

[thumper99]

LOL... Are you done yet? I think I am making progress. I am kind of stuck on #4. I think the formula I have to use is A(t)=20e^-(0.00098)(800). Based on your numbers, do you think this is correct?

[ebaines]

OK, enough struggling. Here's what I get:

1: f(x) = 1+1.6 ln(x+1) = 10
1.6 ln(x+1) = 10-1 = 9
ln(x+1) = 9/1.6 = 5.625
(x+1) = e^5.625 = 277.27
x = 277.27 -1 = 276.27

Put this back into the original formula to check your math:

f(276.27) = 1 + 1.6 ln(276.27+1) = 10, so this answer is correct.

2: You have x*1.1^4 = $1200
so x = 1200/(1.1^4) = $819.62

Again, check your answer:
$819.62 * 1.1^4 = $1200.

3. f(t) = 2000/(1+332.2e^-1.9t)
Plug in t = 9, and chug: I get 1999.975

4. Half-life of t days means that after t days there is 1/2 the amount of mayerial left. So the genetral; formula is:

x = A*0.5^(t/H)

where A is the original amount of material, H id the half life, t is time. And x is what you have left after t time. So pug and chug:

x = 20*(0.5)^(800/710) = 20*.458 = 9.16

5: You are given:
80 = 300*e^(-.00693x), and need to solve for x. Rearrange:

80/300 = e^(-0.00693x)
ln(80/300) = -0.00693x
x = ln(80/300)/(-0.00693) = 190.73

Double check:
300*e(-.00693*190.73) = 300*e^(-1.32) = 80. So the answer looks good.

I suggest you study each of these and make sure you follow along with what I did, and why. Post back if you have questions.