Question

1. Identify each situation in which a quantity grows or decays by a constant percent rate per unit interval. A. The number of cars sold doubles every year. B. The value of a boat decreases by $3000 every 2 years. C. The number of visitors at the Zoo increases by 1,000 each year. D. Each time you start a car engine the remaining engine life decreases by 0.0075%. E. The number of people creating cat videos increases by 15% percent every year. F. Computer technology increases by a factor of 3 every five years. 2. A block of ice weighing 50 kilograms begins to melt. Each hour the block of ice loses 10% of its weight. Let W be the weight in kilograms after melting for t hours. Describe the relationship between W and t?

Answer 1

Explanation:

1) For each situation to grow or decay by a constant percent rate, it must be exponential. Therefore, the correct examples are

A. The number of cars sold doubles every year. It is a 200% growth every year.

D. Each time you start a car engine the remaining engine life decreases by 0.0075%. A case of decay

E. The number of people creating cat videos increases by 15% percent every year.

F. Computer technology increases by a factor of 3 every five years.

2) this is a case of exponential decay. The expression for exponential decay is

y = b(1 - r)^t

y = final value

b = initial value

r = decay rate

t = time

Given that

r = 10% = 10/100 = 0.1

b = 50 kilograms

y = W kilograms

The relationship is

W = 50(1 - 0.1)^t

W = 50(0.9)^t