# 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= 2.5 × 20.04t

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

Pn = 5000 x 20.09t

After what time the population will reach

a. 15000    b. 50000

Solution

Problem 3 :

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

Wt = 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 Wt against t using a and b only

Solution

Problem 4 :

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

Wt = 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 Tt (°C) of a liquid which has been placed in a refrigerator is give by

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

W= W0 x 2-0.0005t

a) the original weight

b)  The weight loss after 1200 years

Solution

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) Wt = Wgrams

i) Initial weight, when t = 0

Wt = 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= 100 x 2-0.04t

a) Initial temperature, T= 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= W0 x 2-0.0005(0)

b)  The weight loss after 1200 years

W1200 = W0 x 0.9597

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