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

It’s Z Bc that’s the only one that starts at 5 and then doubles each year

Answer 2

`A(x)=5\cdot 2^x`

Explanation:

The given scenario can be represented by an exponential growth function. The general form if the exponential growth function is,

`y=a(1+r)^x`

where,

y = the future amount after time x,

a = initial amount,

r = rate of growth.

As here A(x) represents the amount of money after x years with initial deposit of $5 and in each year the amount doubles or duplicates itself i.e r=100% = 1, so the function would be,

`A(x)=5(1+1)^x=5\cdot 2^x`

At the beginning the amount was $5, so the y intercept of the graph will be at 5.