Question

Daniel opens a savings account and deposits $100 into it. Each year, the amount of money in his account increases by 5%. Use the drop-down menus to complete an inequality that can be solved to find how much time, t, it will take for there to be at least $500 in Daniel's account.

Answer 1

`500\leq 100(1.05)^t`

Explanation:

Given,

The initial deposit, P = $ 100,

Annual increasing rate, r = 5 %,

Thus, the amount after t years,

`A=P(1+(r)/(100))^t`

`=100(1+(5)/(100))^t`

`=100(1+0.05)^t`

`\implies A = 100(1.05)^t`

According to the question,

A ≥ $ 500

`\implies 500\leq 100(1.05)^t`

Which is the required inequality that can be used the value of t.