Question

The number of cells in a bacteria colony increases according to the expression t^2-7t-7 with t representing the time in seconds that the colony is allowed to grow in 20°C and t^2-6t-7 when the colony grows at 30°C. After 1 minute, which will be greater in number, a colony at 20°C or 30°C?

Answer 1

Explanation:

To solve this problem, we need to find the number of cells in each colony after 1 minute (60 seconds) and compare them.

For the colony growing at 20°C, the expression for the number of cells is:

N(20°C) = t^2 - 7t - 7

Substituting t = 60 seconds:

N(20°C) = (60)^2 - 7(60) - 7 = 3533

Therefore, the number of cells in the colony growing at 20°C after 1 minute is 3533.

For the colony growing at 30°C, the expression for the number of cells is:

N(30°C) = t^2 - 6t - 7

Substituting t = 60 seconds:

N(30°C) = (60)^2 - 6(60) - 7 = 3563

Therefore, the number of cells in the colony growing at 30°C after 1 minute is 3563.

Comparing these results, we see that the colony growing at 30°C has a greater number of cells after 1 minute than the colony growing at 20°C. Therefore, the colony growing at 30°C will have a greater number of cells than the colony growing at 20°C after 1 minute.