Find the exponential growth function for a population that doubles in sizes every unit of time and that has 40 individuals at time 0
how about
y = 40 (2)^t
To find the exponential growth function, we can use the general form of an exponential function:
P(t) = P0 * (1 + r)^t
Where:
P(t) is the population size at time t
P0 is the initial population size
r is the growth rate
t is the time elapsed
In this case, we know that the population doubles in size every unit of time. This means that the growth rate (r) is 100% or 1.
We are given that the population size at time 0 (P0) is 40.
Substituting these values into the formula, we get:
P(t) = 40 * (1 + 1)^t
Simplifying further:
P(t) = 40 * 2^t
So, the exponential growth function for this population is P(t) = 40 * 2^t.
To find the exponential growth function for a population that doubles in size every unit of time and has 40 individuals initially at time 0, we can use the general form of the exponential growth function: P(t) = P0 * (1 + r)^(t - t0), where P(t) is the population at time t, P0 is the initial population size at time t0, r is the growth rate, and (t - t0) is the time interval.
In this case, since the population doubles in size every unit of time, the growth rate (r) is 1. Since the initial population size is 40 individuals at time 0, we have P0 = 40.
Substituting these values into the formula, we get P(t) = 40 * (1 + 1)^(t - 0).
Simplifying further, we have P(t) = 40 * 2^t.
Therefore, the exponential growth function for this population is P(t) = 40 * 2^t.