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%?
100 - 8.7 = 91.3
so every year multiply by .913
.913^n = 0.60
n log .913 == log 0.60
n = log .6/log .913
about 5.6 years
To determine how long it will take for infant mortality to be reduced by 40%, we can use the concept of compound interest formula, as the reduction rate of 8.7% per year can be seen as a form of compound interest.
The formula we can use is:
Final Value = Initial Value * (1 + Rate)^Time
In this case, the initial value is 100% (since we're starting with the current infant mortality rate), the rate is -8.7% (negative because it represents a decrease), and the final value we want is 60% (since we want to reduce the infant mortality rate by 40%).
Substituting these values into the formula, we have:
60% = 100% * (1 - 8.7%)^Time
Simplifying further, we have:
0.6 = (1 - 0.087)^Time
0.6 = 0.913^Time
To find the value of Time, we can take the natural logarithm (ln) of both sides:
ln(0.6) = ln(0.913^Time)
Using logarithm properties, we can bring Time down as a coefficient:
ln(0.6) = Time * ln(0.913)
Finally, we can calculate Time by dividing both sides of the equation by ln(0.913):
Time = ln(0.6) / ln(0.913)
Using a scientific calculator or software, we can evaluate this expression to find the approximate value of Time. Doing so, we find that it will take approximately 13 years for infant mortality to be reduced by 40% in Senegal, assuming the current reduction rate of 8.7% per year continues.