Question

Each week Thomas will double the amount of money in his bank. What type of function is represented by this situation

Answer 1

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.