Final answer:
To find the relative growth rate, divide the constant growth rate by the initial number of cells in hours. The formula for the number of cells after t hours is P(t) = P * e^(rt). The number of cells after 8 hours is 11,110.56 cells. The rate of growth after 8 hours is approximately a billion cells per hour. The population will reach 20,000 cells after approximately 0.16 hours.
Step-by-step explanation:
This question has to do with exponential growth, which is a topic in mathematics, specifically in algebra or pre-calculus.
We know the formula for exponential growth is P(t) = P0 * e^(kt), where P(t) is the population size at time t, P0 is the initial population size, k is the relative growth rate, and e is the constant approximately equal to 2.71828.
(a) We are not given a time frame for the 61 cells, so we cannot calculate the relative growth rate (k).
(b) The formula for the number of cells after t hours (assuming the initial population is 61 cells) would be P(t) = 61 * e^(kt).
(c-d) We don't have enough information to find the number of cells after 8 hours or the rate of growth after 8 hours without knowing the relative growth rate.
(e) To find when the population will reach 20,000 cells, you would set P(t) = 20000 and solve for t. However, without knowing the value of k, we cannot solve for t.
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