Let n be period in consideration.
Case of RA medicines
Current price of RA medicine=Po=$24
Growth rate=g=22.5%
Period=n
Future price of RA medicine=P1=Po*(1+g)^n=24*(1+22.5%)^n=24*(1.225)^n
Case of diabetes inhaler
Current price of diabetes inhaler=Po=$11
Growth rate=g=13.1%
Period=n
Future price of diabetes inhaler=P1=Po*(1+g)^n=11*(1+13.1%)^n=11*(1.131)^n
We are given
24*(1.225)^n=5*11*(1.131)^n
(1.225/1.131)^n=2.291667
Take natural log both sides
n*Ln(1.225/1.131)=ln(2.291667)
n=ln(2.291667)/Ln(1.225/1.131)=10.39 years
It will take 11 years.
(If we round the time to 10 years, objective is not met. So, we have taken time as 11 years)
The cost of conventional medications for diabetes has risen by an average of 13.1% per year over ...
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