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Lubov Fominskaja [6]
1 year ago
10

1c) Express the function in the form = b^x + c

Mathematics
1 answer:
WARRIOR [948]1 year ago
7 0

The horizontal asymptote is y = 7 and the function is an example of exponential decay

<h3>Express the function in the form = b^x + c</h3>

The equation of the function is given as:

g(x) = -28/[2^(5x + 5)] + 7

Rewrite the equation as follows:

g(x) = -28/[2^(5x) * 2^5] + 7

Evaluate the exponent

g(x) = -28/[2^(5x) * 32] + 7

Divide

g(x) = -7/[2^(5x) * 8] + 7

Rewrite as:

g(x) = -7/[8 * 2^(5x)] + 7

Further, rewrite as:

g(x) = -7/8 * 2^(-5x) + 7

Rewrite properly as:

g(x)=-\frac{7}{8}\left(2^{-5x}\right)+7

<h3>Determine any asymptotes and state whether the function is an example of exponential growth or decay</h3>

We have:

g(x) = -7/8 * 2^(-5x) + 7

Set the radical to 0

g(x) = 0 + 7

Evaluate

g(x) = 7

This represents the horizontal asymptote (it has no vertical asymptote)

Hence, the horizontal asymptote is y = 7 and the function is an example of exponential decay

<h3>Determine the domain and range of the function.</h3>

The function can take any input.

So, the domain is -∝ < x < ∝

We have the horizontal asymptote to be

y = 7

The function cannot equal or exceed this value.

So, the range is x < 7

<h3>Calculate the x-intercept and y-intercept, then sketch the function.</h3>

Set x = 0

g(0) = -7/8 * 2^(-5 * 0) + 7

This gives

g(0) = -7/8 * 2^(0) + 7

Evaluate the exponent

g(0) = -7/8 + 7

Evaluate the sum

g(0) = 49/8

So, the y-intercept is 49/8

Set g(x) = 0

0 = -7/8 * 2^(-5x) + 7

This gives

-7 = -7/8 * 2^(-5x)

Divide by -7

1 = 1/8 * 2^(-5x)

Multiply by 8

8 = 2^(-5x)

Solve for x

x = -0.6

So, the x-intercept is -0.6

See attachment for the sketch

Read more about exponential functions at:

brainly.com/question/2456547

#SPJ1

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Sarah has 2,500 pictures saved to her camera roll. She wants to free up some space on her phone. She will delete a total of 50 p
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Answer:

x = number of days

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Step-by-step explanation:

Hi, to answer this question we have to write an equation:

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A football is kicked into the air. The height of the football can be modeled by the equation
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Answer:

x = 0 and x = 1

Step-by-step explanation:

Given that,

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h = -16x^2 + 16x

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The second one is correct
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Help please!!!!!! And explain ur answer.. I will mark as BRAINLIEST.​
Musya8 [376]

Answer:

The total earning of commission on sales of 85, 000 will be:

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Step-by-step explanation:

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As salesperson earns 5% commission the first 70,000.

\frac{5}{100}\:\times \:70\:000=3500

As the salesperson earns 7% commission on the sales over 70,000.

As 15000 is the sales earning on which he will get commission 7%.

Because

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So the 7% earning of salesperson will on 15000 will be:

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Therefore, the total earning of commission on sales of 85, 000 will be:

3500+1050=4550

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