Working out an exponentially increasing value without a function

Question

This may seem very basic, but I am stumped by this. I have been set this by my Math tutor and I have no idea what to do. I have checked everywhere, but I am pretty sure my tutor made these set of questions himself, so I havn't found anything.

Here's what I have:

\begin{array}{rccc} t: & 0 & 10 & 20 \\ X: & 275 & 440 & x \end{array}

The quantity $X$ is increasing exponentially with respect to time $t$. The table above shows values of $X$ for different values of $t$. Find $X$ when $t = 20$.

I think it would help me more if someone steered me in the right direction rather than just answering the question. I understand the basics of Natural Logs and exponentials so I am not completely blind on the subject. And I can work something like this out if I had the function connecting them, but I dont get how I can work out the relationship. But any help will be greatly appreciated.

Thanks,

-Arch

Answer 1

Hint: You know that $X = Ca^t$ for some numbers $C$ and $a$ (this is what exponentially increasing means). Plug in $t=0$ and $t=10$ to give you two equations that can be used to solve for $C$ and $a$.