# Calc

A model for the food-price index (the price of a representative "basket" of foods) between 1984 and 1994 is given by the function

I(t)=0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33

Where t is measured in years since midyear 1984, so 0≤t≤10, and I(t) is measured in 1987 dollars and scaled such that I(3)=100. Estimate to two decimal places the times when food was cheapest and most expensive during the 1984-1994 period.

1. 👍 0
2. 👎 0
3. 👁 409
1. Given a polynomial function in t where
I(t) = 0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33

We need to find the extrema for 0≤t≤10.

Steps:
find first derivative I'(0), equate to zero. Solve for the zeroes which correspond to the extrema, say t1 and t2.

To distinguish minima from maxima, evaluate I"(t1) and I"(t2) (second derivative).
If I"(t)<0, t is a maximum (most expensive), if I"(t)>0, t is a minimum (cheapest).

Hint:
t1 and t2 are near 1 and 5 resectively, in case you need to solve for zeroes using Newton's method.

1. 👍 0
2. 👎 0
2. dv

1. 👍 0
2. 👎 0
3. 107

1. 👍 0
2. 👎 0
posted by shereen

## Similar Questions

1. ### Calculus

A model for the food-price index (the price of a representative "basket" of foods) between 1984 and 1994 is given by the function I(t)=0.00009045t5+0.001438t4−0.06561t3+0.4598t2−.6270t+99.33 Where t is measured in years since

asked by Danielle on March 25, 2015
2. ### Economics

In 1997, the price of a particular basket of goods was \$2,900. In 1998, the price of the same basket was \$3,300. In 1996, the base year, the price of the basket was \$2,500. (Hint: price index is price indexed to a base year.) A.

asked by Catherine on March 5, 2017
3. ### AP Macroeconomics

1. As an example of a price index, consider the A.C.D.P.I. (a fictitious price index). The associated basket of goods is: Good Quantity Price Coffee 3 lb \$8/lb Bread 3 loaves \$1/loaf Tea 1 lb \$15/lb Aspirin 1 200-tablet bottle

asked by Emily on October 20, 2013
4. ### economics

what is the price index for 2007 when \$675.00 is total expenditure for that year and \$600.00 for 2006. These total expenditures comes from a fixed market basket of goods. How do you calculate price index?

asked by DV on February 1, 2008
5. ### Math

Bosley's Pet Foods buys dog kibbl for \$19.50 per bag, less 40%. The store's overhead is 33 1/3% of the selling price, and the desired profit is 10% of the selling price. (a) At what price per bag should the dog food be sold? (b)

asked by Tha on August 10, 2009
6. ### Macroeconomics

As an example of a price index, consider the A.C.D.P.I. (a fictitious price index). The associated basket of goods is: Good Price Coffee \$8/lb. Bread \$1/loaf Tea \$15/lb. Aspirin \$2/bottle Cola \$6/case A. If the price of coffee

asked by Mary on September 15, 2015
7. ### Economics

The index most widely used by the government and the private sector to measure changes in the cost of living is the (a) the GDP deflator, (b) Producer Price Index, (c) The interest rate, (d) Consumer Price Index

asked by JJ on November 9, 2011
8. ### Pre-Algebra

how do i do these two. irene bought a typewriter at rocklanes in 1988 for \$200.In 1999, she bought the same model of typewriter for \$120.What is the percent decrease in the price of the typewriter. denise bought a typewriter at

asked by Kemmaris on May 14, 2007
9. ### Math

What price do farmers get for the peach crops? in the third week of June, a random sample of 40 farming regions gave a sample mean of \$6.88 per basket. assume that the standard deviation is known to be \$1.92 per basket. find a 90%

asked by Justina on August 7, 2011
10. ### AP Macroeconomics

Assume that the mix of goods in a basket is kept constant for long periods. If the price of one good rises very rapidly over several years, what will happen to the relative importance of the other goods in the basket? Is this a

asked by John on July 3, 2014

More Similar Questions