Answer:
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