Question

Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.

Miguel had $25 in his savings account. His parents will double the amount in his account each month.

If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.

Answer 1

Anita's account had linear growth
Miguel's account had exponential growth.
Miguel's account grew faster because exponential growth is faster than linear growth

Answer 2

Miguel's account will grow fast.

Explanation:

It is given that:

• Anita had $400 in her savings account when she went to college. Her parents will add $200 to her account each month.

Let g(t) represents the function that represent the amount of money in Anita's account in 't' months.

Hence, the function g(t) is given by:

`g(t)=400+200t`

• Miguel had $25 in his savings account. His parents will double the amount in his account each month.

Let f(t) represents the function that represent the amount of money in Anita's account in 't' months.

Hence, the function g(t) is given by:

`f(t)=25* 2^t`

Clearly we could observe that the amount of money in Anita's account have a linear growth and the amount of money in Miguel's account has a exponential growth and we know that exponential function has a more increase i.e. it increases faster than the linear function.

Hence,

Miguel's account will grow fast.