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3 years ago

Fraction from or decimal form but has to be rounded

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

5 0

Answer:

x = $\frac{25}{6}$

Step-by-step explanation:

Given expression is,

$2x-\frac{11}{4}x=-\frac{25}{8}$

$\frac{8x}{4}-\frac{11}{4}x=-\frac{25}{8}$

$\frac{8x-11x}{4}=-\frac{25}{8}$

$-\frac{3x}{4}=-\frac{25}{8}$

$\frac{3x}{4}\times 4=\frac{25}{8}\times 4$

$3x=\frac{25}{2}$

$\frac{3x}{3}=\frac{25}{2}\times \frac{1}{3}$

x = $\frac{25}{6}$

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So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

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$y = 10000 * 1.04^x$ ---- city A

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When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

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$1.04^x > 1.2 * 0.97^x$

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$(\frac{1.04}{0.97})^x > 1.2$

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$\ln(1.07)^x > \ln(1.2)$

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$x\ln(1.07) > \ln(1.2)$

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When city A is at least twice city B, we have the following inequality

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Divide both sides by 0.97^x

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$\ln(1.07)^x \ge \ln(2.4)$

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$x\ln(1.07) \ge \ln(2.4)$

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Answer:

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