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2 years ago

Choose the example of an inverse relationship

1 answer:

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The mathematical explanation is that if f(x) = x + 2 and y (x) = x -2, the relationship is inverse. Also, f(x) = -x and f(x) = 1/x to eliminate a zero value.

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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 $\$800 \times 1.07^t$ .

We want the find the number of years n such that

$\$856 \times 1.07^n = \$1400$

Solve for n :

$856 \times 1.07 ^n = 1400$

$1.07^n = \dfrac74$

$\log_{1.07}\left(1.07^n\right) = \log_{1.07}\left(\dfrac74\right)$

$n \log_{1.07}(1.07) = \log_{1.07} \left(\dfrac74\right)$

$n = \log_{1.07} \left(\dfrac74\right) = \dfrac{\ln\left(\frac74\right)}{\ln(1.04)} \approx \boxed{8.3}$

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