An innovative rural public health program is reducing infant mortality in a certain West African country. Pretend the program in Senegal has been reducing infant mortality at a rate 8.7% per year. How long will it take for infant mortality to be reduced by 40%?
start out at 100
60=100(1-.087)^t
.6=.913^t
take log of each side.
log(.6)=t*log(.913)
t= 5.6 years
To determine how long it will take for infant mortality to be reduced by 40% in Senegal's rural public health program, we can use the annual reduction rate of 8.7%.
The formula to calculate the time it takes for a value to be reduced by a certain percentage annually is:
Time = log (Final Value / Initial Value) / log (1 - Annual Rate)
Let's use this formula to find the time it takes for infant mortality to be reduced by 40%:
Annual Rate = 8.7% = 0.087
Reduction Percentage = 40% = 0.4
Time = log(1 - 0.4) / log(1 - 0.087)
Calculating this equation gives us the number of years it will take for infant mortality to be reduced by 40%.
Time = log(0.6) / log(0.913)
Using a scientific calculator or any calculator that allows logarithmic calculations, we find:
Time ≈ 13.17
Therefore, it would take approximately 13.17 years for infant mortality to be reduced by 40% in Senegal's rural public health program.