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Nadya [2.5K]
3 years ago
6

In 1990, the rate of change of the world population was approximately 0.09125 billion per year (or approximately 1 million peopl

e every four days). The world population was estimated to be 5.3 billion in 1990.
Write an equation to model the population, P (in billions), in terms of t, where t is the number of years since 1990 (t = 0 corresponds to 1990)

A. P= 5.3 + 0.09125t

B. P= 5.3t + 0.09125

C. P= -5.3 + 0.09125t

D.P= -5.3t + 0.09125
Mathematics
2 answers:
Rasek [7]3 years ago
8 0

Answer:

A

Step-by-step explanation:

babunello [35]3 years ago
6 0

Answer: Option A

P = 5.3 + 0.09125t

Step-by-step explanation:

Note that for the initial year, 1990, the population was 5.3 billion.

The exchange rate is 0.09125 billion per year. In other words, each year there are 0.09125 billion more people.

In year 2 there will be 0.09125 * 2 billion people

In year 3 there will be 0.09125 * 3 billion people

In year 4 there will be 0.09125 * 4 billion people

In year t there will be 0.09125 * t billion of people

So the equation that models the number of people that there will be as a function of time is:

P = P_0 + rt

Where P_0 is the initial population

P_0 = 5.3 billion

r is the rate of increase

r = 0.09125 billion per year

finally the equation is:

P = 5.3 + 0.09125t

The correct answer is option A.

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Option D:

$y=\frac{5x-2}{x}

Solution:

Given function:

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To find the inverse of the function.

<u>Inverse of a function:</u>

<em>If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back to x.</em>

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Interchange the variables x and y.

$x=\frac{-2}{y-5}

Now, solve for y.

Multiply both sides by (y - 5).

$x(y-5)=-\frac{2}{y-5}(y-5)

Cancel the common factors, we get

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Divide by x on both sides.

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Add 5 on both sides.

$y=-\frac{2}{x}+5

$y=-\frac{2}{x}+\frac{5}{1}

To make the denominator same, multiply the 2nd term by \frac{x}{x}.

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