Is this answer correct?

Mathematics

2 answers:

AVprozaik [17]2 years ago

8 0

Yes,it is correct and so is your written answer

ycow [4]2 years ago

6 0

Yes. 25.6 is correct. And the written work looks great. Very thorough.

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Find the value of x from the equation

Jobisdone [24]

$\dfrac{8^{3x}}{2^{10}}=\dfrac{4^{2x}}{16} \\\dfrac{2^{3(3x)}}{2^{10}}=\dfrac{4^{2x}}{4^2} \\2^{9x-10}=4^{2x-2} \\2^{9x-10}=2^{2(2x-2)} \\2^{9x-10}=2^{4x-4} \\9x-10=4x-4 \\5x-6=0 \\5x=6 \\\boxed{x=\dfrac{6}{5}}$

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r3t40

3 0

3 years ago

In 2010, the population of a town was 8500. The population decreased by 4.5% each year.

Soloha48 [4]

Answer:

This is a problem in exponential decay.

a) If a town's population decreases by 4.5% every year that also means that the town's population decreases by a factor of .955 each year. (1 - .045 = .955)

So, after 5 years, the town's population is:

8,500 * .955^5 which equals 6,752.

So, basically, after t years, the town's population equals

8,500 * .955^t where t is the number of years that have passed since the year 2010.

b) population = 8,500 * .955 ^ (number of years since 2010)

7,000 / 8,500 = .955 ^ (number of years since 2010)

0.8235294118 = .955 ^ (number of years since 2010)

To solve for (number of years since 2010) we take logs of both sides

log (0.8235294118 ) = number of years since 2010 * log(.955)

-0.0843208857 = number of years since 2010 * -0.0199966284

-0.0843208857 / -0.0199966284 = number of years since 2010

4.2167551422 = number of years since 2010