Question

What model describes the relationship between the amount of money in an account and time, given that the money doubles every month?

linear
quadratic
cubic
exponential

Answer 1

The model that describes the relationship between the amount of money in an account and time, given that the money doubles every month is:

Exponential

Explanation:

Let the initial amount of money be: x

• i.e. amount of money in first month= x

• Hence, if money doubles every month then the amount of money in second month is: 2x

• In third month it will be:
  `2* 2x=2^2x`

• In fourth month it will be:
  `2* 2^2x\\\\=2^3x`

and so on,

Hence, the amount of money in nth month is:

`2^(n-1)x`

As the amount of money increases by a fixed multiplicative rate i.e. 2.

Hence, the model is:

Exponential.

Answer 2

If we have a common ratio every set amount of time (and not a common difference or addition), this is an exponential relationship. An exponential equation would have a form like Money = (1000)(2)^(# of months), where every additional month would cause the money amount to double.