Can someone solve these?

Mathematics

1 answer:

Kaylis [27]3 years ago

4 0

Answer:

Step-by-step explanation:

You need to find out what x and y is first then you can solve it

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The population of a city grows exponentially at rate of 8% per year.Find the number of years it takes for the population to be d

Ilya [14]

Answer:

It will take 9 years for the population to double

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

$P=P_o(1+r)^t$

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The population of a city grows at a rate of r=8% = 0.08 per year. We are required to find when (t) the population will double, or P=2Po.

Substituting in the equation:

$2P_o=P_o(1+0.08)^t$

Simplifying:

$2=(1.08)^t$

Taking logarithms:

$\log 2=\log (1.08)^t$

Applying the exponent property of logs:

$\log 2=t\log (1.08)$

Solving for t:

$\displaystyle t=\frac{\log 2}{\log (1.08)}$

Calculating:

$t\approx 9$

It will take 9 years for the population to double

8 0

3 years ago

write an equation in point slope form of the line that passes through the point (5/6 , 0) and has a slope of m=-3

lyudmila [28]

$(\stackrel{x_1}{\frac{5}{6}}~,~\stackrel{y_1}{0})~\hspace{10em} \stackrel{slope}{m}\implies -3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-3}(x-\stackrel{x_1}{\frac{5}{6}})$