Jen, a biologist, is growing bacterial cultures at different temperatures as part of her research. The number of cells in the culture growing at 25 °C is given by the polynomial 2+4+4, where t is the time elapsed in minutes. The number of cells in the second culture growing at 35°C is modeled by the polynomial 2+ 4. She needs to measure the success of the 25 °C culture over the 35 °C culture. Find the polynomial representing how many more cells are in the 25 °C culture for time t. How many more cells are there after 15 minutes?

1) The polynomial representing the number of more cells that are in the 25°C culture for time, 't' is;

h(t) = 4·t

2) There are 60 more cells in the 25 °C culture after 15 minutes

Step-by-step explanation:

The polynomial that gives the number of cells growing in a culture at 25°C is given as follows;

f(t) = t² + 4·t + 4

The polynomial that gives the number of cells growing in a culture at 35°C is given as follows;

g(t) = t² + 4

The number of more cells that are in the 25°C culture at time, 't' is given by the following polynomial, h(t);

h(t) = f(t) - g(t)

∴ h(t) = (t² + 4·t + 4) - (t² + 4)

h(t) = t² - t²+ 4·t + 4 - 4 = 0 + 4·t + 0

∴ h(t) = 4·t

Therefore, the polynomial representing the number of more cells that are in the 25°C culture at time, 't', h(t) = 4·t

Therefore, the number of more cells that are in the 25°C culture after 15 minutes is h(15) = 4 × 15 = 60

The number of more cells that are in the 25°C culture after 15 minutes = h(15) = 60 more cells

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