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 % per year. How long will it take for infant mortality to be reduced by 34 %?
Well, if we put on our math hats and do some calculations, we can figure this out!
Let's assume that the current infant mortality rate is 100%. If the program in Senegal reduces it by 8% per year, it means that each year, the rate drops to 92% of what it was the previous year.
To find out how long it would take for infant mortality to be reduced by 34%, we need to determine how many times the rate needs to be multiplied by 0.92 to get to 66% (100% - 34%).
So, let's do the math, shall we?
0.92^x = 0.66
To solve this equation, I'll need my trusty quote book. Ah, here it is! "Mathematics is like love; a simple idea, but it can get complicated."
After some calculations, it turns out that it will take approximately 8 years for infant mortality to be reduced by 34% with the program in Senegal.
To calculate how long it will take for infant mortality to be reduced by 34%, we need to divide the desired reduction rate by the annual reduction rate.
The reduction rate for the program in Senegal is 8% per year. Therefore, the time it takes to achieve a 34% reduction can be calculated as follows:
Time = Desired Reduction Rate / Annual Reduction Rate
Time = 34% / 8%
Now we can calculate the value:
Time = 4.25 years
Therefore, it will take approximately 4.25 years for infant mortality to be reduced by 34% in Senegal through this program.
To find out how long it will take for infant mortality to be reduced by 34%, we can use the concept of exponential decay.
The program in Senegal is reducing infant mortality at a rate of 8% per year. This means that the infant mortality rate is decreasing by 8% of the previous year's rate each year.
We can represent this decrease as a decimal value by subtracting 8% (0.08) from 1: 1 - 0.08 = 0.92
Now, let's denote "t" as the number of years it will take for infant mortality to be reduced by 34%. If the infant mortality is reduced by 8% per year, it means that the final infant mortality rate will be 34% less than the initial rate.
So, we have: 1 - 0.08t = 0.66
To solve for "t," we can isolate the variable by subtracting 1 from both sides of the equation: -0.08t = -0.34
Now, let's divide both sides of the equation by -0.08: t = -0.34 / -0.08
By performing the division, we get: t = 4.25
Therefore, it will take approximately 4.25 years for infant mortality to be reduced by 34% in the rural public health program in Senegal.
.92^x = .66
x = log.66/log.92 = 4.99
or, 5 years