Answer: 28 years
Step-by-step explanation:
Given
The equation showing the value of the bag after x years is [tex]C=25(1.025)^x[/tex]
If the price of the bag increased by 2.5%, from the equation, we can deduce that
Initial cost of the bag is 25
Double of the initial value is 50
Insert it in the equation
[tex]\Rightarrow 50=25(1.025)^x\\\Rightarrow 2=1.025^x\\\text{Taking natural log}\\\Rightarrow \ln 2=x\ln (1.025)\\\\\Rightarrow x=\dfrac{\ln 2}{\ln 1.025}\\\\\Rightarrow x=28.07\approx 28[/tex]
It will take 28 years
