EXPONENTIAL GROWTH AND DECAY WORD PROBLEMS WORKSHEET

Problem 1 :

The weight of bacteria in a culture t hours after it has been established is given by

W_t = 2.5 × 2^0.04t

grams. After what time will the weight reach

a. 4 grams     b. 15 grams

Solution

Problem 2 :

The population of bees in hive, t hours after it has been discovered, is given by 

P_n = 5000 x 2^0.09t

After what time the population will reach 

a. 15000    b. 50000

Solution

Problem 3 :

The weight W_t grams of radioactive substance remaining after t years is given by 

W_t = 1000 x 2^-0.03t grams. Find

i)  The initial weight

ii)  The weight after 

a) 10 years    ii) 100 years     iii) 1000 years

iii)  Graph W_t against t using a and b only

Solution

Problem 4 :

The weight of radioactive substance after t years is given by the formula 

W_t = W₀  x 3^-0.003t grams. Find

i)  The initial weight

ii)  The percentage remaining after

a) 100 years    ii) 500 years     iii) 1000 years

Solution

Problem 5 :

The temperature T_t (°C) of a liquid which has been placed in a refrigerator is give by

T_t = 100 x 2^-0.04t

a) the initial temperature

b)  The temperature after 

i) 10 minutes     ii)  25 minutes      iii)  60 minutes

c) Find how long it takes for the temperature to reach 20°C.

Solution

Problem 6 :

The weight W_t (°C) of a radioactive substance remaining after t years is given by the formula

W_t = W₀ x 2^-0.0005t

a) the original weight

b)  The weight loss after 1200 years 

Solution

Answer Key

1)  a) Approximately 17 hours.

b)  Approximately 64.6 hours.

2)  a)  Approximately 17.6 hours.

b)  t = 36.9 hours

3)  i) W₀ = 1000 grams

ii)  The weight after 

a) i)  W₁₀ = 813 grams   ii)  W₁₀₀ = 125 grams

iii)  W₁₀₀₀ = 9.313 x 10^-7

4)  i) W_t = W₀ grams

i) Initial weight, when t = 0

W_t = W₀  x 3^-0.003(0)

ii)  The weight after 

i) 100 years    ii) 500 years     iii) 1000 years

i)  when t = 100, 71.9 % of W₀

ii)  when t = 500, 19.2 % of W₀

iii)  when t = 1000, 3.7 % of W₀

5)  T_t = 100 x 2^-0.04t

a) Initial temperature, T₀ = 100

b)  The temperature after 

i) 10 minutes, T₁₀ = 75.78

ii)  25 minutes, T₂₅ = 50

iii)  60 minutes, T₆₀ = 18.94

6)  a)  W_t = W₀ x 2^-0.0005(0)

b)  The weight loss after 1200 years 

W₁₂₀₀ = W₀ x 0.9597