MATH 122 TEST 1
10/10/2011 FALL, 2011
Remember to keep your work neat and orderly. Show all of your work. NO WORK = NO CREDIT! Read each
question carefully and be sure to answer the question that was asked. Solve all equations algebraically and then
𝑟
evaluate using your calculator. Good luck!
𝐵 = 𝑃(1 + 𝑛)𝑛𝑡
𝐵 = 𝑃𝑒 𝑟𝑡
Name:____________________________________________________________
pts
1. You deposit $3,000 in an account paying 2.6% interest.
a. If the interest is compounded continuously, how much do you have after 9 years?
4
b. If the interest is compounded twice a year, how long (to the nearest hundredth of a year)
until you have $4,100?
7
2. Put in vertex form by completing the square. Identify the vertex. 𝑦 = −5𝑥 2 − 50𝑥 + 17
7
Vertex:____________
3. At the beginning of 1990, the size of a forest was 800 acres. One third of the area of the forest
is being cleared every five years.
a. Find a model for the area of the forest as a function of time (define variables!).
5
b. What percent (to 5 significant digits) of the forest is being cleared each year?
4
4. Put the function 𝑦 = 7𝑒 −.23𝑡 in the form 𝑦 = 𝑎𝑏 𝑡 . Find b to five significant digits.
5. If 𝑅(𝑢) = 1 − 3𝑢
and
𝑊(𝑎) = 3𝑎 − 𝑎2 , find and simplify 𝑊(𝑅(𝑥)).
6. Expand and write your answer without any exponents or radicals
2
7. Let 𝑃(𝑦) = {𝑦 − 2
5−𝑦
9
a. Find 𝑃 ( ).
2
ln
1
5
( √𝑥 2 )(𝑥+𝑦)3
−3 ≤ 𝑦 < −1
−1 < 𝑦 ≤ 3 }
𝑦>3
b. Sketch the graph of P.
8. Solve for x without using a calculator. Leave your answer as a fraction.
log 𝑥 − log(𝑥 − 2) = 2
5
6
5
2,6
7
9. My real-estate taxes were $4,200 in 2001 and are $5,300 in 2011.
a. Build a linear model for my taxes over time (define your variables!).
b. Build an exponential model for my taxes over time.
5
5
c. Use both models to see what each predicts my taxes will be in 2018 to the nearest dollar.
6
10.The number of asthma cases is increasing by 9.1% every 4 years. How long will it take for the
number of cases to double (to the nearest hundredth of a year)? Give the model!
7
11.Find x to 5 significant digits:
a. 24 = 17 + 3 ln(5 − 2𝑥)
b. 7𝑒 3𝑥+2 − 200 = 1000
7,7
12.Find the equation of a parabola (in any form) that opens down and has zeros at x = 4 and -5.
5