Question

Math help questions
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Answer 1

25 years

Explanation:

total = before × percent ( in decimal ) × time

1400 = 800 × 0.07 × t

1400 = 56 × t

1400 ÷ 56 = 25

t = 25

Hope this was helpful!

Answer 2

After 1 year, the initial investment increases by 7%, i.e. multiplied by 1.07. So after 1 year the investment has a value of $800 × 1.07 = $856.

After another year, that amount increases again by 7% to $856 × 1.07 = $915.92.

And so on. After t years, the investment would have a value of
`\$800 * 1.07^t`.

We want the find the number of years n such that

`\$856 * 1.07^n = \$1400`

Solve for n :

`856 * 1.07 ^n = 1400`

`1.07^n = \frac74`

`\log_(1.07)\left(1.07^n\right) = \log_(1.07)\left(\frac74\right)`

`n \log_(1.07)(1.07) = \log_(1.07) \left(\frac74\right)`

`n = \log_(1.07) \left(\frac74\right) = (\ln\left(\frac74\right))/(\ln(1.04)) \approx \boxed{8.3}`