Exponential Function Word Problems

Name:

Class:

Date:

Show your work for each problem.

1.
A phone loses 15% of its value every year. Which factor $b$ do you use in the model $V(t) = a \cdot b^t$ ?
1. a)0.15
2. b)1.15
3. c)0.85
4. d)85
2.
The number of fish in a lake is modeled by $P(t) = 1200 \cdot 1.04^t$ , where $t$ is in years. What does the number $1.04$ tell you?
1. a)The population grows by 4% each year
2. b)The population grows by 104% each year
3. c)The population grows by 4 fish each year
4. d)There are 1.04 fish at the start
3.
Each list shows the values of a quantity for $t = 0, 1, 2, 3$ . Which list follows an exponential model?
1. a)5; 10; 15; 20
2. b)5; 8; 11; 14
3. c)5; 10; 20; 40
4. d)5; 9; 13; 17
4.
You invest 2000 dollars at 6% annual interest, compounded quarterly. Which model gives the amount $A$ after $t$ years?
1. a) $A = 2000 \cdot 1.015^{t}$
2. b) $A = 2000 \cdot 1.06^{4t}$
3. c) $A = 2000 \cdot 1.24^{t}$
4. d) $A = 2000 \cdot 1.015^{4t}$
5.
A car bought for 20000 dollars loses 10% of its value every year. Four students computed its value after 4 years. Which result is correct?
1. a)12000
2. b)29282
3. c)2
4. d)13122
6.
A video has 500 views, and the number of views doubles every day. How many views does it have after 6 days?
7.
A substance has a half-life of 5 hours. A sample starts with 80 mg. How many mg are left after 20 hours?
8.
You deposit 1000 dollars at 8% annual interest, compounded quarterly. How much is in the account after 5 years? Round to the nearest cent.
9.
1500 dollars are invested at 5% per year, compounded continuously. Use $e^{0.5} \approx 1.6487$ . How much is the investment worth after 10 years? Round to the nearest dollar.
10.
A table gives $y = 80$ at $t = 0$ , $y = 120$ at $t = 1$ , $y = 180$ at $t = 2$ and $y = 270$ at $t = 3$ . Decide whether it is linear or exponential, then find the exact value of $y$ at $t = 5$ .
11.
A laptop costs 1200 dollars and loses 20% of its value every year. What is it worth after 3 years?
12.
On Monday, 4 students know a new dance challenge. Every day the number of students who know it triples. How many students know it 4 days later?
13.
You invest 3000 dollars at 5% annual interest, compounded semiannually (twice a year). How much do you have after 6 years? Round to the nearest cent.
14.
A radioactive material has a half-life of 5 years. A sample has 640 g. How many grams are left after 15 years?
15.
A patient gets 500 mg of a medicine. The amount in the blood decays continuously at a rate of 10% per hour, so $A(t) = 500 \cdot e^{-0.1t}$ . Use $e^{-0.2} \approx 0.8187$ . How many mg are left after 2 hours? Round to the nearest mg.
16.
Bank A pays 5% per year, compounded annually. Bank B pays 5% per year, compounded monthly. You deposit 10000 dollars for 3 years. How much more does Bank B pay? Round every amount to the nearest cent.
17.
A town had 2000 inhabitants. Two years later it had 2880. Assume exponential growth $P(t) = 2000 \cdot b^t$ ( $t$ in years). Find $b$ , the yearly growth rate, and the population after 4 years (rounded to whole inhabitants).
18.
The value of a car is $V(t) = 18000 \cdot 0.88^t$ dollars, $t$ years after it was bought. Interpret the model, then find after how many whole years the value first drops below 10000 dollars.