12.4 Problems
Find the derivative
1.
𝑦 = 𝑒 4𝑥
3.
𝑦 = −8𝑒 3𝑥
5.
𝑦 = −16𝑒 2𝑥+1
8.
𝑦 = 𝑒 −𝑥
11. 𝑦 = 4𝑒 2𝑥
2 −4
2
13. 𝑦 = 𝑥𝑒 𝑥
15. 𝑦 = (𝑥 + 3)2 𝑒 4𝑥
17. 𝑦 =
19. 𝑦 =
𝑥2
𝑒𝑥
𝑒 𝑥 −𝑒 −𝑥
𝑥
21. 𝑝(𝑡) =
10,000
9+4𝑒 −0.2𝑡
33.
𝑦=
𝑥2
3 +2)
(𝑥
𝑒
48. The concentration of pollutants (in grams per liter) in the east fork of the Big Weasel River is
approximated by
𝑃(𝑥) = 0.04𝑒 −4𝑥
Where x is the number of miles downstream from a paper mill that the measurement is taken. Find the
following values.
a. The concentration of pollutants 0.5 miles downstream
b. The concentration of pollutants 1 mile downstream
c. The concentration of pollutants 2 miles downstream
Find the rate of change of concentration with respect to distance for the following distances
d. 0.5 miles
e. 1 mile
f. 2 miles
53. The age/weight relationship of female Arctic foxes caught in Svalbard, Norway, can be estimated by
the function
𝑀(𝑡) = 3102𝑒 −𝑒
−0.022(𝑡−56)
Where t is the age of the fox in days and M(t) is the weight of the fox in grams
a. Estimate the weight of a female fox that is 200 days old
b. Use M(t) to estimate the largest size that a female fox can attain.
c. Estimate the age of a female fox when it has reached 80% of its maximum weight
63. Suppose a person is going up in a hot air balloon. The surrounding air temperature in degrees
Fahrenheit decreases with height according to the formula
𝑇(ℎ) = 80𝑒 −0.000065ℎ
Where h is the height in feet. How fast is the temperature decreasing when the person is at a height of
1000 feet and rising at a height of 800 ft/hr?