Daniel opens a savings account and deposits $100 into it. Each year, the amount of money in his account increases by 5%. Use the

Question

2 years ago

13

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.

Mathematics

2 answers:

shtirl [24] · Answer 1 · 2022-02-27T05:10:48+03:00

shtirl [24]2 years ago

5 0

it will take him 33 years to reach $500

Alina [70] · Answer 2 · 2022-02-27T06:46:09+03:00

Alina [70]2 years ago

4 0

Answer:

$500\leq 100(1.05)^t$

Step-by-step explanation:

Given,

The initial deposit, P = $ 100,

Annual increasing rate, r = 5 %,

Thus, the amount after t years,

$A=P(1+\frac{r}{100})^t$

$=100(1+\frac{5}{100})^t$

$=100(1+0.05)^t$

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

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.