the number of cells in a bacteria colony increases according to a polynomial expression that depends on the temperature. The expression for the number of bacteria is t^2+4t+4 when the the tempature of the colony is 20c and t^2+3t+4 when the colony grows at 30c. t represents the time in seconds that the colony grows at the given tempature.

After 1 minute, the population in a colony at 20ºC will be greater than the population in a colony at 30ºC.

Explanation:

The specific question is added on the comments section: After 1 minute, will the population be greater in a colony at 20ºC or 30ºC? Explain

Solution

How will the colonies compare in size?

To answer this you can either evaluate each polynomial at the corresponding time and then compare or you can subtract the polynomials and then evaluate the resulting polynomial.

I choose the second opion:

20ºC 30ºC

↓ ↓

t² + 4t + 4 - (t² + 3t + 4) = t² - t² + 4t - 3t + 4 - 4 = t

The difference is t (remember that this is number of bacteria).

Evaluate when the time is 1 minute.

In the polynomials, t is in seconds. Then, convert 1 minute to seconds:

1 min * 60 s/min = 60s

Then, t = 60 bacteria is the difference.

Thus, the colony has 60 more bacteria when the temperature is 20ºC than when the temperature is 30ºC.

In fact, since t is always greater than 0, the colony at 20ºC will always have more bacteria than the colony at 30ºC.