I need help finding the correct formula after finding the doubling time and continuous percentage. I got the doubling time of 24 days and the continuous percentage of 2.89%.
Homework asking use the doubling time to find the continuous percent growth rate and give a formula of the function.
For the formula it says round all coefficients to 4 decimal places if required.
I attempted to do it but I don't think my method is working
I put P = ln(2) / 24
I don't know what the original problem was, but if the doubling time is 24 days, the formula for the amount present after t days is
A(t) = Ao * 2^(t/24)
Since 2 = e^ln2, that is equivalent to
A(t) = Ao * e^(ln2/24 t)
To find the continuous percent growth rate given the doubling time, you can use the formula:
r = ln(2)/d
where "r" is the continuous percentage growth rate and "d" is the doubling time in the same units as the growth rate. In your case, you have a doubling time of 24 days.
So, to calculate the continuous percentage growth rate, substitute the values into the formula:
r = ln(2)/24
Now, let's calculate the value of "r":
r = 0.0287 (approximately)
Now that you have found the continuous percentage growth rate (rounded to four decimal places), you can proceed to find the formula for the function.
The formula for the exponential growth function is given by:
P(t) = P₀ * e^(rt)
where "P(t)" represents the population at time "t," "P₀" is the initial population, "e" is the mathematical constant approximately equal to 2.71828, "r" is the continuous percentage growth rate, and "t" is the time.
In your case, since you are given the continuous percentage growth rate as 0.0287 (approximately), the formula becomes:
P(t) = P₀ * e^(0.0287t)
Remember to round all coefficients to four decimal places as required by the homework instructions.
Therefore, the formula for the function with the given doubling time and continuous percentage growth rate is:
P(t) = P₀ * e^(0.0287t)