Question

Stella initially put $5 into a piggy bank. Over the next few years she continued to put all of her coins in the piggy bank, such that each year the amount of money in the piggy bank doubled. Determine the equation that represents this situation and use it to decide which of the following graphs represents the amount of money, A(x), in Stella's piggy bank after x years.

Answer 1

Answer: Z.

Step-by-step explanation:

They want you to figure formula then find right graph, but do it fastest way. If it doubles each year, graph can't be straight line, eliminate Y.

A(0) has to be $5, eliminate W. A(1) has to be double A(0), eliminate X. Check: Z shows A(1) is 10, A(2) is 20.

Answer 2

Answer:

The equation is A(x) = 5(2)ˣ and the graph is Graph Z.

Step-by-step explanation:

Equations on compounding interest (which this essentially is) are of the form

A(x) = p(1+r)ˣ, where p is the amount of principal, r is the interest rate and x is the amount of time.

Since Stella begins with $5, the principal is 5.

Since the amount of money doubles each year, this means we add an extra 100%; this makes r equal to 1.

This gives us the equation

A(x) = 5(1+1)ˣ = 5(2)ˣ

This graph will not be linear, as there is not a constant rate of change (there are different amounts added every year).

She begins with $5.  This means the y-intercept of the graph will be 5.

After 1 year, the amount of money doubles; this makes it 10.  The only graph that is not linear and goes through (0, 5) and (1, 10) is graph Z.