Answer: a. 12.4 years
Step-by-step explanation:
Function to represent exponential growth continuously:
[tex]A=A_0e^{rt}[/tex] ...(i)
, where [tex]A_0[/tex] = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.
As per given , we have
[tex]A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500[/tex]
To find : t
Put all values in (i) ,
[tex]3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}[/tex]
Taking natural log on both sides
[tex]\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4[/tex]
Hence, it would take 12.4 years.
so, the correct option is a. 12.4 years .
