Select all the expressions equivalent to:

Mathematics

1 answer:

olchik [2.2K]2 years ago

8 0

Answer:

5(4a + 2b)

10(2a + b)

2(10a + 5b)

Step-by-step explanation:

we are trying to find equations equivalent to (20a + 10b), so distribute

5(4a + 2b) = 20a +10b YES

10(2a + b) = 20a +10b YES

2(10a +5) = 20a + 10 NO

2(10a + 5b) = 20a +10b YES

5(4a - 2b) = 20a - 10b NO

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The birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)= 1450e0.018t people per year, fi

Cerrena [4.2K]

Answer:

38,674.This area represents the increase in population over a 10-year period.

Step-by-step explanation:

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.

The birth rate is graphed in green and the death rate is graphed in blue.

To find the area, take the integral of the difference of the functions:

$\int\limits^{10}_0 {2300e^{0.021t} - 1450e^{0.018t} } \, dt \\\\\frac{2300e^{0.021t}}{0.021} - \frac{1450e^{0.018t}}{0.018} \\\\(\frac{2300e^{0.21}}{0.021} -\frac{1450e^{0.18}}{0.018} ) - (\frac{2300}{0.021}- \frac{1450}{0.018} ) \\\\135117.12 - 96442.51 \\\\38,674$