Question

The population of bacteria is directly proportional to the temperature. There are about 10 million bacteria at 20 degrees Celsius.

Create a formula for this. What type of variation is this? What is k? How many bacteria will there be at 30 degrees celsius? Where else would I use this?

Answer 1

Population is directly proportional to the temperature.

This implies

P T

=> P = kT

where k is the constant of proportionality

When T = 20 degree celsius, P = 10 million

Therefore,

10 = k(20)

=> k = 10 / 20

=> k = 1 / 2

Therefore, the formula is

P = (1/2) T

The relationship between population and temperature is linear. Therefore, the variation is linear.

k = 1/2

Substituting T = 30 degrees Celsius

P = (1/2)(30) = 15 million

Therefore, there are about 15 million bacteria at 30 degrees Celsius