Need help with a couple problems

[mrcutty]

The problems are:

1. Given the polynomial f(x)=2x3-5x2-4x+3, find the solutions if the function is completed as:
(The numbers behind the x represent square)
f(x)=0
f(x=2)=0
f(2x)=0

2. Today you visit the R&D department of a pharmaceutical manufacturer. The people in the lab have to calculate the recommended dosage of the products they are developing. Medicine is potency of the dosage declining over a period of time. The function N(t)=(0.8t+1000)/(5t+4), where t=>15 gives the body concentration N(t) in parts per million, of a certain dosage of medication after time t, in hours.

a. Find the horizonal asymptote of the graph and complete the following statement: N(t) appriacges ? as t approaches infinitity.
b. Explain the meaning of the answer to a) in terms of the medical dosage application.

3. A retailer you spoke with in New York City's fashion district imports haute conture from Eurpean designers. One of the accommodations which must be considered when importing fashion from other countries is the difference in the size charts. A function that will convert dress sizes in the United States to those in Italy is g(x) = 2(x+12).
a. Find the dress sizes in Italy that correspond to sizes 6, 10 and 14 in the United States.
b. Fina a formula for the inverse of the function
c. Use the inverse function to find the dress sizes in the United States that correspond to 36, 44, and 60 in Italy.

4. Last week's profits from a dry cleaners was $2000. Suppose the $2000 is invested at interest rate k, compounded continuously, and grows to $2983.65 in 5 years.

a. What is the interest rate?
b. Find the exponential grown function
c. What will the balance be after 10 years?
When will the $2000 double?

Thanks in advance for any help you can give.
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[stapel]

1) I will assume that, by "square", you mean "exponent", rather than "to the power 2" (which is the definition of "squared"), so the function is:

. . . . .f(x) = 2x³ - 5x² - 4x + 3

If so, set the function equal to zero, and solve:

. . . . .f(x) = 0 = 2x³ - 5x² - 4x + 3

I don't know what you might mean by "f(x=2)=0". But for f(2x), plug "2x" in for "x" in the polynomial, and simplify. Then set the result equal to zero, and solve by whatever method(s) you have learned.

2) To find the horizontal asymptote, apply the formula they gave you. To do the "explain" part, think about what the function measures.

3) (a) Since the input is "dress sizes in the United States", what does "x" represent? So how would you find the Italian values for the US values of 6, 10, and 14? (b) Finding the inverse of a linear function is fairly straightforward. Where in the process are you stuck? (c) Once you have the inverse function, just plug these values into it, and simplify to get the answers.

4) Plug P = 2000, A = 2983.65, and t = 5 into the continuous-growth formula. Solve for the interest rate. Use this to write the formula. Then plug in "10" for t to find the balance in ten years. Plug "4000" in for A and solve for the value of t to find the doubling time.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.