Steve - you answered this question earlier for someone else and gave them the formula for how to answer it. I have the same problem in my homework and have used the formula you gave, but have got an answer that does not appear in the answer options.
I got 12.75
Would you be able to show your workings and help me to get the correct answer please?
the population growing at an annual rate r will triple in a time t given by the formula t = ln 3/r If the growth rate remains constant and equals 9% per year, how long will it take the population of the town to triple?
a. 6 . 6 years
b. 1 years
c. 5 . 3 years
d. 2 . 2 years
e. 12.2 years
Yeah, I noticed that. I can't figure why the closest answer is so far off. To get 12.2 years, r needs to be 9.58%
amount = original * (1+r)^t
3 = (1+r)^t
ln 3 = t ln (1+r)
t = ln 3 / ln(1+r)
r = .09
t = ln 3 / ln(1.09)
t = 1.0986 / .086178
t = 12.74 years
======================
check
3 = 1 * 1.09^12.74 ??????
3 = 2.997 yes that will do
To find the correct answer, we need to use the given formula:
t = ln(3)/r
where t represents the time it takes for the population to triple and r is the annual growth rate.
In this case, the annual growth rate, r, is 9% expressed as a decimal, which is 0.09.
Let's substitute the values into the formula and calculate the time, t:
t = ln(3) / 0.09
To calculate the natural logarithm of 3, you can use a scientific calculator or an online calculator that has a natural logarithm function. When we calculate ln(3), we get approximately 1.0986.
Now, let's substitute the value of ln(3) into the equation:
t = 1.0986 / 0.09
When we divide 1.0986 by 0.09, we get approximately 12.207.
Therefore, the correct answer is e. 12.2 years.
It seems like you made a minor mistake in your calculations, which led to the answer 12.75 instead of 12.2. Double-check your calculation process to make sure you have used the correct formula and carried out the calculations accurately.