Answer:
The value of the quantity after 21 days is 2,347.59.
Step-by-step explanation:
The exponential growth function is

A= The number of quantity after t days
= initial number of quantity
r= rate of growth
t= time in days.
A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 2 weeks = 14 days.
Now A= (2×830)= 1660
= 830
t = 14 days
r=?
Now plug all value in exponential growth function




![\Rightarrow (1+r)=\sqrt[14]{2}](https://tex.z-dn.net/?f=%5CRightarrow%20%20%281%2Br%29%3D%5Csqrt%5B14%5D%7B2%7D)
![\Rightarrow r=\sqrt[14]{2}-1](https://tex.z-dn.net/?f=%5CRightarrow%20%20r%3D%5Csqrt%5B14%5D%7B2%7D-1)
Now, to find the quantity after 21 days, we plug
= 830, t= 21 days in exponential function
![A=830( 1+\sqrt[14]{2}-1)^{21}](https://tex.z-dn.net/?f=A%3D830%28%201%2B%5Csqrt%5B14%5D%7B2%7D-1%29%5E%7B21%7D)
![\Rightarrow A=830(\sqrt[14]2)^{21}](https://tex.z-dn.net/?f=%5CRightarrow%20A%3D830%28%5Csqrt%5B14%5D2%29%5E%7B21%7D)



The value of the quantity after 21 days is 2,347.59.