Practice Page
Directions: Read carefully.
1.
Given the equation: y = 95(1.25)x
a) Does this equation represent exponential growth or decay?
Choose:
growth
decay

b) What is the initial value?
Choose:
25
75
95
125

c) What is the rate of growth or decay?
Choose:
25%
1.25%
0.25%
95%

 

 

2.
The first year of a walk to raise money for local animal shelters had 500 walking participants. The participation has increased each year by 5%.
Which choice is an exponential growth function that will model this situation?
 
Choose:
y = 500(1 + 0.5)x
y = 500(1 - 0.05)x
y = 500(0.95)x
y = 500(1.05)x

 

 

3.
During a laboratory experiment,
E. coli bacteria is increasing continuously at a growth rate of 1.8% per minute.
a) If there are currently 150 million bacteria, which
exponential function will model this experiment?

 

 

 
Choose:
y = 150e0.018•t
y = 150e0.18•t
y = 150e1.8•t
y = 150e18•t

b) What will be the number of bacteria 5.8 minutes from now, to the nearest tenth of a million?
Choose:
154.3 million
166.5 million
426.1 million
5130097.9 million

 

 

4.
A total of 500 players participate on the first day of an Internet on-line game. After day 5, there are 10,000 players participating.
a) Using the model, A = A0ekt to represent this situation, which choice is the value of k?
Choose:
ln(50) / 5
ln(25) / 5
ln(20) / 5
ln(500) / 5

 

b) Re-write the model equation to place it in the form y = abt and then into the form y = a(1+r)t.
Using this new form, determine the rate of growth per day of the number of players participating in this game.
Which choice is the approximate rate of growth per day?
Choose:
18%
46%
82%
97%

 

 

5.
A new electric bike costs $1,179. If it depreciates by 24% per year, what is the e-bike worth at the end of 5 years?

 Choose:
$150.47
$298.94
$345.64
$504.74
 

 

 

6.
The doubling time of a population of mosquitoes is every 7 days. There are initially 200 mosquitoes.

a) Which exponential function can be used to model this situation?
Choose:
A = 200(2)7 t
A = 200(2)t / 7
A = 200(7)2t y A = 200(7)t / 2
 
 

b) How many mosquitoes will there be in 3 weeks?
Choose:
1,600
3,680
8,795
9,800

 

 

7.
Iodine-131 is a radioactive isotope used in the treatment of thyroid conditions. It has a half-life of 8 days. Half-life is the amount of time it takes for half of the substance to decay (disappear). If a patient is given 20 mg of iodine-131, how much of the substance will remain in the body after 32 days?
 Choose:
8 mg
5 mg
2.5 mg
1.25 mg
radioactive
 

 

 

8.
The kitchen temperature is 73º F. Chocolate chip cookies fresh from the oven register at 350º F. After 8 minutes, the temperature of the cookies drops to 152º F.
Newton's Law of Cooling states:
   T(t) = Ta + (T0 - Ta)e-kt

T(t) = temperature of object at time t
Ta = surrounding air temperature
T0 = initial temperature of object
k = decay constant

 

 

 

a) Determine the value of k for this situation.
 Choose:


b) Determine the temperature of the cookie after 15 minutes.
Choose:
89.2º
99.4º
112.2º
114.9º

c) A "warm" cookie is defined to be a cookie of a temperature of 120º F. How much time, after coming out of the oven, would be needed (to the nearest tenth of a minute) for these cookies to be described as "warm"?
Choose:
9.4 minutes
10.2 minutes
11.3 minutes
12.7 minutes



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