Question

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

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?

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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

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