Question

A recent study showed that the number of Australian homes with a computer doubles every 8 months. Assuming that the number is increasing continuously, at approximately what monthly rate must the number of Australian computer owners be increasing for this to be true?

A. 68%
B. 8.66%
C. 0.0866%
D. 0.002%

Answer 1

B. 8.66%

Explanation:

In this case we have to evaluate the following formula:

n = e ^ (k * t)

where n would be the growth rate, we are told that it doubles therefore it is 2.

k is the monthly rate and time, 8 months.

Solved for k, we are left with:

ln (n) = k * t

k = ln (n) / t

replacing we have:

k = ln (2) / t = 0.693 / 8

k = 0.0866

If we take this to a percentage it would be 0.0866 * 100 = 8.66%

Therefore the answer is B.