Answer:
An exponential growth.
Step-by-step explanation:
We know that each week, Thomas will double the amount of money in his bank.
Let's assume that in week 0, he has an amount A of money in his bank.
After one week, in week number 1 (w = 1), the amount of money is doubled, so if we define the function M(w) as the amount of money as a function of the number of weeks, we will have:
M(1) = 2*A
After another week, in w = 2, the amount of money is doubled again, so here we have:
M(2) = 2*(M(1)) = 2*(2*A) = A*2^2
After another week, at w = 3, the amount of money is doubled again:
M(3) = 2*(M(2)) = 2*(A*2^2) = A*2^3
We already can see the pattern here, we can expect that for the week w, the amount of money in the account is given by:
M(w) = A*2^w
This is an exponential equation (an exponential growth to be more specific), so the type of function that is represented by this situation is an exponential growth.
