Suppose that a colony of fruit °ies is growing according to the
exponential law P(t) = P0ekt, and suppose that the size of the colony triples
in 11 days. Determine the growth constant k. [You may leave your answer
as a fraction, with logarithm(s) in it.]
I need help. i am so lost
so you are solving
3 = 1(e^11k)
ln3 = ln(e^11k)
ln3 = 11k(lne), but lne = 1
k = ln3/11
wow thanks a lot. i am glad you helped me out thanks again
To determine the growth constant k, we need to use the given information that the size of the colony triples in 11 days.
According to the exponential law, the general formula for the population size P at a given time t is given by P(t) = P0 * e^(kt), where P0 is the initial population size, k is the growth constant, and t is the time in days.
In this case, we are given that the size of the colony triples, which means the final population size (P) is three times the initial population size (P0). We can express this relationship mathematically as:
3P0 = P0 * e^(k * 11)
To solve for the growth constant k, we need to isolate it in the equation. Let's do that step by step:
1. Divide both sides of the equation by P0 to eliminate it on the right side:
3 = e^(k * 11)
2. Take the natural logarithm (ln) of both sides of the equation:
ln(3) = ln(e^(k * 11))
3. We can use the property of logarithms that ln(e^x) = x, so the right side simplifies to:
ln(3) = k * 11
4. Divide both sides of the equation by 11 to solve for k:
k = ln(3) / 11
Therefore, the growth constant k is equal to ln(3) / 11, which can be left as a fraction with logarithm in it.