# exponential growth/decay word problem

• Jun 8th 2008, 01:07 AM
cityismine
exponential growth/decay word problem
The department of health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing exponentially at an annual rate of 9%. The first year that statistics were collected, 5000 cases were reported.

a. Estimate the # of cases reported after 7 years.

b. Estimate the # of years, to the nearest tenth, required for the # of reported cases to rise to 11,000.
• Jun 8th 2008, 01:37 AM
janvdl
Quote:

Originally Posted by cityismine
The department of health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing exponentially at an annual rate of 9%. The first year that statistics were collected, 5000 cases were reported.

a. Estimate the # of cases reported after 7 years.

b. Estimate the # of years, to the nearest tenth, required for the # of reported cases to rise to 11,000.

a) $\displaystyle A = (5000) \left( 1 + \frac{9}{100} \right) ^{7}$

b) $\displaystyle 11 000 = (5000) \left( 1 + \frac{9}{100} \right) ^{n}$

$\displaystyle n = \log_{(5000) \left( 1 + \frac{9}{100} \right)} 11000$