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4 years ago

Which graph represents a quadratic function that has one real zero?

Mathematics

2 answers:

umka2103 [35]4 years ago

7 0

Answer:

Step-by-step explanation:

on edge

zhenek [66]4 years ago

6 0

Answer:

Step-by-step explanation:

The graph attached below represent the quadratic function with one real solution.

If the graph cuts the x -axis at only one point then it can be said there is only one -solution to the given equation.

If the graph does not touch the x-axis then their is no real solution.

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Task 2 a. Do some research and find a city that has experienced population growth. Determine its population on January 1st of a

Galina-37 [17]

Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate

<h3>The equation of a city that has experienced a population growth</h3>

The initial population of the city is 10000, and the growth rate of the population is 4%.

So, the exponential equation is:

$y = 10000 * 1.04^x$

<h3>The equation of a city that has experienced a population decline</h3>

The initial population of the city is 12000, and the decay rate of the population is 3%.

So, the exponential equation is:

$y = 12000* 0.97^x$

<h3>The similarities in the equations</h3>

The similarity in both equations is that, they both represent exponential function.

<h3>The year the population of city A exceeds B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A exceeds city B, we have the following inequality

$10000 * 1.04^x > 12000 * 0.97^x$

Divide both sides by 10000

$1.04^x > 1.2 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{0.97})^x > 1.2$

$1.07^x > 1.2$

Take the natural logarithm of both sides

$\ln(1.07)^x > \ln(1.2)$

This gives

$x\ln(1.07) > \ln(1.2)$

Solve for x

$x > \frac{\ln(1.2)}{\ln(1.07)}$

$x > 2.69$

This means that, the population of city A will exceed city B after 3 years

<h3>The year the population of city A will be at least twice of city B</h3>

In (a) and (b), we have:

$y = 10000 * 1.04^x$ ---- city A

$y = 12000* 0.97^x$ --- city B

When city A is at least twice city B, we have the following inequality

$10000 * 1.04^x \ge 2 * 12000 * 0.97^x$

$10000 * 1.04^x \ge 24000 * 0.97^x$

Divide both sides by 10000

$1.04^x \ge 2.4 * 0.97^x$

Divide both sides by 0.97^x

$(\frac{1.04}{ 0.97})^x \ge 2.4$

$1.07^x \ge 2.4$

Take the natural logarithm of both sides

$\ln(1.07)^x \ge \ln(2.4)$

This gives

$x\ln(1.07) \ge \ln(2.4)$

Solve for x

$x\ge \frac{\ln(2.4)}{\ln(1.07) }$

$x\ge 12.9$

This means that, the population of city A will be at least twice city B after 13 years

Read more about exponential functions at:

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Answer: No he is incorrect as 1 inch is equal to 4 feet.

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