Exponential Decay

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Show your work for each problem.

1.
Which function shows exponential decay?
1. a) $y = 40 \cdot 0.75^t$
2. b) $y = 40 \cdot 1.2^t$
3. c) $y = 40 \cdot 3^t$
4. d) $y = 40 + 0.75t$
2.
A quantity decreases by $15\%$ every year. What is the decay factor $b$ ? Write it as a decimal.
3.
For $f(t) = 500 \cdot 0.6^t$ , by what percent does $f$ decrease each period?
1. a)6%
2. b)60%
3. c)0.4%
4. d)40%
4.
Function 1 is $y = 150 \cdot 1.04^t$ and function 2 is $y = 150 \cdot 0.96^t$ . Which one shows decay?
5.
An exponential model has decay factor $0.93$ . What is the decay rate in percent? Type the number only (for example 5 for $5\%$ ).
6.
A laptop costs 1000 dollars and loses $20\%$ of its value each year. What is it worth after 2 years (in dollars)?
7.
A phone costs 600 dollars and loses $20\%$ of its value each year. Which expression gives its value after $t$ years?
1. a) $600 \cdot 1.2^t$
2. b) $600 \cdot 0.8^t$
3. c) $600 - 0.2t$
4. d) $600 \cdot 0.2^t$
8.
Analyze the model $f(t) = 2000 \cdot 0.7^t$ and find $f(2)$ .
9.
A quantity loses $20\%$ in every period. What percent of the starting amount is left after 4 periods? Type the number only, with two decimal places.
10.
A car is bought for 20000 dollars and loses $10\%$ of its value each year. What is it worth after 3 years (in dollars)?
11.
Which statement about $y = 80 \cdot 0.75^t$ is NOT true?
1. a)The initial value is 80
2. b)It reaches 0 after 4 periods
3. c)After one period, y = 60
4. d)It decreases by 25% each period
12.
A patient takes 500 mg of a medicine. The body removes $10\%$ of the remaining amount every hour. How many milligrams are left after 5 hours? Round to the nearest whole milligram.
13.
A machine is worth 10000 dollars. Model A: it loses 1500 dollars per year. Model B: it loses $15\%$ per year. Which model gives the higher value after 5 years?
1. a)Model B (about 4437)
2. b)Both give the same value
3. c)Model A (2500)
4. d)Both are worth 0
14.
Coffee is $85°C$ in a room at $20°C$ . In a simple model, the difference between the coffee and the room shrinks by $10\%$ every minute. What is the coffee's temperature after 3 minutes, in °C? Round to one decimal place.
15.
A machine costs 12000 dollars. Plan A: it loses 1500 dollars per year. Plan B: it loses $20\%$ per year. After 4 years, how many dollars higher is the value under plan A than under plan B?
16.
A bicycle's value drops from 400 to 324 in 2 years, losing the same percent each year. What is the yearly percent decrease? Type the number only.
17.
A scooter costs 1000 dollars and loses $20\%$ of its value each year. After how many full years is it worth less than 450 dollars for the first time?
18.
A patient receives 800 mg of a medicine. Each hour the body removes $40\%$ of the amount still present. How many milligrams are left after 3 hours, and what percent of the dose is that?