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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.

Respuesta :

it will take him 33 years to reach $500

Answer:

[tex]500\leq 100(1.05)^t[/tex]

Step-by-step explanation:

Given,

The initial deposit, P = $ 100,

Annual increasing rate, r = 5 %,

Thus, the amount after t years,

[tex]A=P(1+\frac{r}{100})^t[/tex]

[tex]=100(1+\frac{5}{100})^t[/tex]

[tex]=100(1+0.05)^t[/tex]

[tex]\implies A = 100(1.05)^t[/tex]

According to the question,

A ≥ $ 500

[tex]\implies 500\leq 100(1.05)^t[/tex]

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

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