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3 years ago

1/2x - 3/4y=-2 Solve for Y

1 answer:

5 0

$\frac{1}{2}x-\frac{3}{4}y=-2\ \ \ |Add\ \frac{3}{4}y\\\\
\frac{1}{2}x=-2+\frac{3}{4}y\ \ \ |Add\ 2\\\\
\frac{1}{2}x+2=\frac{3}{4}y\ \ |*\frac{4}{3}\\\\
y=\frac{4}{3}(\frac{1}{2}x+2)\\\\
\boxed{y=\frac{2}{3}x+\frac{8}{3}}$

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3 years ago

Suppose a population is growing by 8% each year. How many years will it take the population to double?

Doss [256]

ANSWER

$\text{9 years}$

EXPLANATION

We want to find the number of years that it will take the population to double.

To do this, we have to apply the exponential growth function:

$y=a(1+r)^t$

where y = final value

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r = rate of growth

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For the population to double, it means that the final value must be 2 times the initial value:

$y=2a$

Substitute the given values into the function above:

$\begin{gathered} 2a=a(1+\frac{8}{100})^t \\ \frac{2a}{a}=(1+0.08)^t=1.08^t \\ 2=1.08^t \end{gathered}$

To solve further, convert the function from an exponential function to a logarithmic function as follows:

$\log _{1.08}2=t$

Solve for t:

$\begin{gathered} \frac{\log _{10}2}{\log _{10}1.08}=t \\ \Rightarrow t=9\text{ years} \end{gathered}$

It will take 9 years for the population to double.

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1 year ago