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2 years ago

A population of paramecia, P, can be modeled using the exponential

Mathematics

1 answer:

Ksivusya [100]2 years ago

4 0

The appropriate domain of the population function is 0 ≤ t ≤ 14

<h3>How to determine the domain?</h3>

The function is given as:

P(t) = 3(2)^t

From the question, we understand that the maximum time is 2 weeks.

2 weeks in days is 14 days

This means that the function is valid for 14 days i.e. t = 0 to 14

Hence, the appropriate domain of the population function is 0 ≤ t ≤ 14

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Using long division to find the quotient, what changes do you first

lora16 [44]

Answer:

$\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4$

Step-by-step explanation:

Given

$Dividend = 125x^3 - 8$

$Divisor = 5x - 2$

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

$\frac{125x^3}{5x} =25x^2$

Write $25x^2$ at the top

Multiply $5x - 2$ by $25x^2$

$= 125x^3 - 50x^2$

Subtract from 125x^3 - 8

i.e.

$125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8$

Step 2:

Divide 50x^2 by 5x

$\frac{50x^2}{5x} = 10x$

Write $10x$ at the top

Multiply $5x - 2$ by $10x$

$= 50x^2 - 20x$

Subtract from 50x^2 - 8

i.e.

$50x^2 - 8 - (50x^2 - 20x) = 20x - 8$

Step 3:

Divide 20x by 5x

$\frac{20x}{5x} = 4$

Write $4$ at the top

Multiply $5x - 2$ by $4$

$= 20x - 8$

Subtract from 20x - 8

i.e.

$20x - 8 - (20x - 8) = 0$

Hence:

$\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4$

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