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3 years ago

I don't understand #54.. Please help

Mathematics

1 answer:

tensa zangetsu [6.8K]3 years ago

6 0

It's just asking you to graph. So youre going to graph 3 things. You plug in the numbers that work for the given equation. You just have to graph it. For example 0 is not less than -3 so no need to do anything there

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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:

brainly.com/question/11464095

3 0

3 years ago

What is the width of Averi's area model? (See picture)

shepuryov [24]

Answer:

Width = x² + 5x - 4

Step-by-step explanation:

By the definition of an area model,

Area = Width × greatest common factor

Since, Area = 4x² + 20x - 16

And greatest common factor = 4

4x² + 20x - 16 = 4(Width)

By dividing both the sides of the equation by 4,

$\frac{4x^2+20x-16}{4}=\frac{4(\text{Width})}{4}$

x² + 5x - 4 = Width

Therefore, width = (x² + 5x - 4) will be he answer.

8 0

3 years ago

How many gallons of milk containing 1% fat is mixed with milk containing 4% fat to obtain a 15 gallon mixture

Novosadov [1.4K]

Answer:

Step-by-step explanation:

milk dont have fat but it contains 5% of milk

7 0

3 years ago

what is the 4 called

IrinaVladis [17]

Answer:

The Index

Step-by-step explanation:

A radical expression is composed of three parts:

The Radicand - The number or term under the horizontal bar of the radical symbol.

Radical Symbol - The Radical Symbol √

Index - The number near the "check" part of the radical symbol.

In the given expression, 4 is the index. We are supposed to find the 4th root of x to the third power.

Hope this helps.

6 0

3 years ago

A conical tank has height 3 m and radius 2 m at the top. Water level is rising at a rate of 1.8 m/min when it is 1.5 m from the

Free_Kalibri [48]

Answer:

5.655 m³/min

Step-by-step explanation:

Halfway from the bottom of the tank, the radius is half that at the top, so is 1 m. That means the surface area of the water at that point is ...

A = πr² = π(1 m)² = π m²

The rate of flow of water into the tank is the product of this area and the rate of change of depth:

flow rate = area × (depth rate of change)

= (π m²) × (1.8 m/min) = 1.8π m³/min

flow rate ≈ 5.655 m³/min

7 0

3 years ago