Can you help me with this? I don't know how to figure it out.
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
What's to figure out? They gave you the exact formula you need. 9% growth means it grows by a factor of 1.09 each year, so
t = ln3/ln1.09 = ?
That gives me 12.75 though which isn't one of the answers? Did I do the calculation wrong?
In3/In1.09=12.75
should I choose answer 12.2?
To find out how long it will take for the population to triple, we can use the given formula: t = ln(3)/r.
In this case, the growth rate remains constant at 9% per year, which can be expressed as 0.09 (since 9% is equal to 0.09 as a decimal). Therefore, we substitute this value into the formula:
t = ln(3) / 0.09
To solve for t, we need to find the natural logarithm of 3. The natural logarithm can be found using a calculator or a mathematical software. The value of ln(3) is approximately 1.0986.
Now we substitute this value back into the formula:
t = 1.0986 / 0.09
Dividing 1.0986 by 0.09 gives us approximately 12.2067.
Therefore, the population will triple in approximately 12.2067 years.
So the correct answer is e. 12.2 years.