Exponential Growth and Decay Quiz

Grade 11 · Math · Quiz

10 questions on growth/decay models, half-life, doubling time, and compound interest.

Questions

1. Which value of b makes f(x) = 3*b^x an exponential growth function?

   1. b = 0.5
   2. b = 1
   3. b = 1.2
   4. b = 0
   Show answer

   Answer: b = 1.2

   Growth requires b > 1. Only b = 1.2 satisfies this.

2. A car worth $20,000 depreciates 15% per year. What is it worth after 2 years?

   1. $14,450
   2. $17,000
   3. $16,000
   4. $15,000
   Show answer

   Answer: $14,450

   f(2) = 20000(0.85)^2 = 20000 x 0.7225 = $14,450.

3. f(t) = 100e^(-0.02t). What is f(0)?

   1. 0
   2. -0.02
   3. 100
   4. e
   Show answer

   Answer: 100

   f(0) = 100e^0 = 100 x 1 = 100.

4. A bacteria culture doubles every 3 hours. Starting from 50 bacteria, how many after 9 hours?

   1. 200
   2. 300
   3. 400
   4. 450
   Show answer

   Answer: 400

   9 hours = 3 doubling periods. 50 x 2^3 = 50 x 8 = 400.

5. Continuous compound interest: A = Pe^(rt). Find A if P=1000, r=0.06, t=5.

   1. $1300.00
   2. $1349.86
   3. $1060.00
   4. $1416.18
   Show answer

   Answer: $1349.86

   A = 1000 * e^(0.30) = 1000 x 1.34986 = $1349.86.

6. A substance has half-life of 20 days. After 60 days, what fraction remains?

   1. 1/4
   2. 1/8
   3. 1/6
   4. 1/3
   Show answer

   Answer: 1/8

   60 / 20 = 3 half-lives. (1/2)^3 = 1/8.

7. What is the doubling time for continuous growth rate k = 0.1?

   1. 6.93 years
   2. 10 years
   3. 1 year
   4. 0.1 years
   Show answer

   Answer: 6.93 years

   t_double = ln(2)/0.1 = 0.693/0.1 = 6.93 years.

8. The graph of f(x) = 2^x has a horizontal asymptote at:

   1. y = 1
   2. y = 2
   3. y = 0
   4. x = 0
   Show answer

   Answer: y = 0

   As x -> -inf, 2^x -> 0 but never reaches it; the asymptote is y = 0.

9. Which equation models 10% annual growth from an initial value of 500?

   1. f(t) = 500(0.9)^t
   2. f(t) = 500(1.1)^t
   3. f(t) = 500 + 10t
   4. f(t) = 500e^t
   Show answer

   Answer: f(t) = 500(1.1)^t

   Discrete growth: f(t) = a(1+r)^t = 500(1.10)^t.

10. Solve for t: 80 = 160e^(-0.04t). Round to nearest whole number.

    1. t = 17
    2. t = 10
    3. t = 25
    4. t = 20
    Show answer

    Answer: t = 17

    0.5 = e^(-0.04t) -> ln(0.5) = -0.04t -> -0.693 = -0.04t -> t = 17.3, rounds to 17.

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