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3 years ago

Using distributive property create an equivalent expression to 40+4x

1 answer:

4 0

Hi there!

To create an expression that uses the distribution property which can be simplified into 40 + 4x, we can find a factor between 40 and 4:

Since both 40 and 4 is divisible by 4,

40 / 4 = 10
4 / 4 = 1

We can put the 4 on the outside of the parenthesis, and put the quotients inside the parenthesis. And since the expression is in addition, we should include the addition symbol as the operation inside the parenthesis.

4(10 + x)
would be your answer.

Hope this helps!

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Shalnov [3]

<h2>Exponential Functions</h2>

Exponential functions are typically organized in this format:

$f(x) = a*c^x$

To find the equation given the graph of an exponential function:

Identify the horizontal asymptote
⇒ <em>asymptote</em> - a line towards which a graph appears to travel but never meets
⇒ If the horizontal asymptote is not equal to 0, we add this at the end of the function equation.
Identify the y-intercept
⇒ This is our <em>a</em> value.
Identify a point on the graph and solve for <em>c</em>

<em />

<h2>Solving the Question</h2>

Identify the horizontal asymptote

In this question, it appears to be x = 0.

Identify the y-intercept

The y-intercept is the value of <em>y</em> at which the graph appears to cross the y-axis. In this graph, it appears to be 100. This is our <em>a</em> value. Plug this into $f(x) = a*c^x$ :

$f(x) = 100*c^x$

Solve for <em>c</em>

We can use any point that falls on the graph for this step. For instance, (1,50) appears to be a valid point. Plug this into our equation and solve for <em>c</em>:

$f(x) = 100*c^x\\50 = 100*c^1\\50 = 100*c\\\\c=\dfrac{1}{2}$

Plug <em>c</em> back into our original equation:

$f(x) = 100*(\dfrac{1}{2})^x$

<h2>Answer</h2>

$f(x) = 100*(\dfrac{1}{2})^x$

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2 years ago

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3 years ago

Suppose a city with population 800,000 has been growing at a rate of 7% per year. If this rate continues, find the population of

djverab [1.8K]

Answer:

1,752,000

Step-by-step explanation:

1. First you have to take the 7% and multiply that by the years whish is 17 so that way you know your total percentage of growth which is 119%

2. Second you then need to find how much 1% is to find out our total growth in population so you take 800,000 and divide that by 100 since there's only 100% and you get 8,000.

3. Now you take the 8,000 and multiply that by the percentage of the growth that you have which is 8,000*119 and you get 952,000

4. Lastly all you have to do is add the growth of the population to the population you already have so 800,000+952,000=1,752,000

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