Math 4111
Test 1
Spring 1996

No books, notes etc. are permitted.
Show all your work! Box in your answers!
The test has 6 problems on 3 pages. Read the problems carefully!

Problem 1 (15 points)   Find an equation y=f(x) representing the following data:

x	4.1	4.2	4.3	4.4
y	23.5	23.3	23.1	22.9

Problem 2 (15 points)   When a cold yam is put into a hot oven, the temperature of the yam rises. The rate, R (in degrees Fahrenheit per minute), at which the temperature rises, is governed by Newton's Law of Heating, which says that the rate R is proportional to the temperature difference between the yam and the oven. If the oven has a constant temperature of 400 $^\circ$F and the temperature of the yam is $H\ ^\circ$F, write a formula for R as a function of H, and then sketch its graph.

Problem 3 (20 points)   A rabbit population is known to double every 10 months. How long will it take for the rabbit population to triple?

Problem 4 (20 points)   Find all solutions to the following equations with three-digit accuracy:

1.

$$2\cdot 5^t=7\cdot 3^{2t}$$

2.

$$x+2=11 \log x$$

Problem 5 (15 points)   Which of the following three functions is of the form $y(x)=k\cdot x^3$? Also find the constant k.

x	f(x)	g(x)	h(x)
2.5	3.594	9.375	9.488
3.0	6.210	13.500	14.880
3.5	9.861	18.375	23.336
4.0	14.720	24.000	36.598
4.5	20.959	30.375	57.397

Problem 6 (15 points)   A population of animals varies sinusoidally between a high of 1050 on January 1 and a low of 550 on July 1. Find a formula for the animal population as a function of time, measured in months since the start of the year!