Math 150-06: Quiz #2 (1.4 – 2.3) Name:
Show as much work as possible to get full credit.
1. Describe each of the following function’s growth. Do not simply draw a picture; rather give the “definition” of the growth. (4 points each)
(a) Linear growth
growth by a constant average rate of change (slope)
(b) Exponential growth
growth by a constant percent change
(c) Logistic growth
exponential growth that levels off
2. The value of a certain investment is currently $40000. (5 points each)
(a) If this investment grows by $2250 each year, give a model for the value of the investment x years from now.
V1(x) = 40000 + 2250x dollars in x years
(b) If this investment grows by 4.28% each year, give a model for the value of the investment x years from now.
V2(x) = 40000(1.0428)x dollars in x years
(c) Use both models to estimate the value of the investment 5 years from now.
V1(5) = %51250
V2(5) = $49324.77
3. Describe the concavity of the graph for each of the following model type. (3 points each)
(a) Exponential
always concave up
(b) Logarithmic
when increasing – concave down; when decreasing – concave up
(c) Logistic
has both a concave up section and a concave down section
4. For each of the following discrete functions, find the most appropriate model (from those we have studied), determine whether the model should be discretely interpreted or interpreted without restriction, and then find the indicated value. (8 points each)
(a) The amount of chlorofluorocarbons (CFC’s) released into the atmosphere (in millions of kilograms) in various years is shown in the table. Estimate the amount released in 1985.
Year / 1982 / 1984 / 1986 / 1988CFC’s / 337.4 / 359.4 / 376.5 / 392.8
C(x) = 9.165x + 320.7 million kg x years after 1980
Discretely interpreted because input is years
1985 = C(5) = 366.525 million kg
(b) The average length (in centimeters) of a girl x months old is shown in the table. Estimate the average length of a girl that is 30 months old.
x / 4 / 10 / 18 / 27 / 35 / 42Length / 62 / 72 / 83 / 89 / 93 / 96
L(x) = 40.196 + 14.784ln(x) cm at x months
Can be used without restriction
30 months = L(30) = 90.48cm
(c) The reaction activity (measured in Units per 100 microliters = U/100µL) is measured during the first 18 minutes after the mixture in an experiment reached 95°C. Estimate the reaction activity at 12.5 minutes.
Minutes / 0 / 2 / 4 / 6 / 8 / 10 / 12 / 14 / 16 / 18Activity / 0.1 / 0.1 / 0.25 / 0.6 / 1 / 1.4 / 1.55 / 1.75 / 1.9 / 1.95
A(x) = 1.937/(1+29.06e-.l421x) U/100μL after x minutes
Can be used without restriction
A(12.5) = 1.68 U/100μL