Modeling with Exponential and Logarithmic Equations Quiz

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The amount of a sample remaining after t days is given by the equation mc004-1.jpg, where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 60% of its original amount of Fermium-257. The half-life of Fermium-257 is about 100 days. About how old is the sample?

52 days
60 days
74 days
136 days
C
Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

Makayla invests her money 1 year longer.
Makayla invests her money 2 years longer.
Calvin invests his money 1 year longer.
Calvin invests his money 2 years longer.
B
A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation mc010-1.jpg to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?

6.1
6.6
7.2
23.1
---not B
Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years
2.0 years
3.1 years
5.0 years
A
An equation for the depreciation of a car is given by y = A(1 - r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

3.3 years
5.0 years
5.6 years
6.6 years
D
The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution whose hydrogen ion concentration is mc015-1.jpg?

1.0
2.9
8.7
9.3
C
A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

2.5 days
5.0 days
46.6 days
66.7 days
C
The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?
---not A
A car was purchased 6 years ago for $25,000. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?
A y=25,000(.89)^6
The loudest sound measured one night during a hockey game was 112 dB. The loudest sound measured during a hockey game the next night was 118 dB. What fraction of sound intensity of the second game was the sound intensity of the first game?
---not C