SOLUTION: 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%

Question 1077445: 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 number of cases reported after 7 years.
b. Estimate the number of years, the nearest tenth, required for the number of reported cases to rise to 11,000.
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The number of cases is growing by 9% each year, so after 7 years, we have:
a)N=5000*(1+.09)^7=5000*1.82803912081669=9140.195 cases.
b)11000=5000*(1.09)^t
2.2=1.09^t
ln 2.2=ln 1.09^t=t ln 1.09
t=ln 2.2/ln 1.09=9.1492044 years after the first cases were reported. ☺☺☺☺
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