How much does each person get?

Find a formula for the exponential function passing through the points (-1,5/3) and (3, 135).

Artyom0805 [142]

The expression y = 4.998 · $e^{1.098\cdot x}$ is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).

<h3>How to derive an exponential function that passes through two given points</h3>

Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:

$y = A \cdot e^{B \cdot x}$

Where:

A - y-Intercept of the exponential function.
B - Growth factor
x - Independent variable.
y - Dependent variable.

Which is equivalent to the following logarithmic expression:

㏑ y = ㏑ A + B · x

If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:

㏑ (5 / 3) = ㏑ A - B

㏑ 135 = ln A + 3 · B

Then, we solve the system by numerical methods:

㏑ A = 1.609 (A = 4.998), B = 1.098

And the exponential function is equal to y = 4.998 · $e^{1.098\cdot x}$ .

To learn more on exponential functions: brainly.com/question/11487261

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6 0

2 years ago

Please help!

qwelly [4]

It could be -1, 1, and 2

5 0

3 years ago

Read 2 more answers

If tatianna works 3hrs a day on school days and make $123.75 a week what is her hourly rate?

madreJ [45]

<u><em>Answer:</em></u>

Her hourly rate is $8.25

<u><em>Explanation:</em></u>

Tatianna works 3 hours a day on school days and makes a total of $123.75 in a week

There are 5 school days in a week

<u>We are given that:</u>

She works for 3 hours a day each of those days

<u>Therefore:</u>

Total number of hours worked = hours worked daily * number of days

Total number of hours worked = 3 * 5 = 15 hours in a week

<u>The equation used to calculate Tatianna's earnings is:</u>

Amount she makes in a week = Total number of hours worked * hourly rate

<u>Now, we substitute with the givens to get the hourly rate as follows:</u>

Amount she makes in a week = Total number of hours worked * hourly rate

123.75 = 15 * hourly rate

Hourly rate = $8.25

6 0

3 years ago

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 37 farming regions gave a sa

Airida [17]

Answer:

(a) 90% confidence interval for the population mean price (per 100 pounds) is ($6.34, $7.42)

Margin of error is $0.54

(b) The sample size is 172

(c) 90% confidence interval for the population mean cash value is ($1902.51, $2225.51)

Step-by-step explanation:

Confidence interval = mean + or - (t×sd)/√n

Mean = $6.88 per 100 pounds, sd = $1.94 per 100 pounds, n = 37, degree of freedom = n-1 = 37-1 = 36

t-value corresponding to 36 degrees of freedom and 90% confidence level is 1.688

(a) Lower limit = $6.88 - (1.688×$1.94)/√37 = $6.88 - $0.54 = $6.34

Upper limit = $6.88 + (1.688×$1.94)/√37 = $6.88 + $0.54 = $7.42

90% confidence interval is ($6.34, $7.42)

Margin of error (E) = (t×sd)/√n = (1.688×$1.94)/√37 = $0.54

(b) √n = (t×sd)/E = (1.688×$1.94)/0.25 = 13.10

n = 13.10^2 = 172

1 ton = 2000 pounds

15 tons = 15×2000 = 3000 pounds = 300 hundred pounds

Mean = $6.88×300 = $2064, sd = $1.94×300 = $582

Lower limit= $2064 - (1.688×$582)/√37 = $2064 - $161.51 = $1902.49

Upper limit= $2064 + (1.688×$582)/√37 = $2064+$161.51 = $2225.51

90% confidence interval is ($1902.49, $2225.51)

Margin of error = (1.688×$582)/√37 = $161.51

3 0

3 years ago

pls help ill give a hundred points. select the correct answer from the drop down menu A(1,3),B(5,3),and D(1,-2) are three vertic

tankabanditka [31]

<h2>Question ↷</h2>

A(1,3),B(5,3),and D(1,-2) are three vertices of rectangle ABCD the coordinates of vertex C are select from the drop down menu (5,2),(-5,1),(5,-2),(2, -5)

<h2>Answer↷</h2>

(5,-2)

<h2>Solution ↷</h2>

we know that,

the midpoint of the diagonals of a rectangle bisect each other,

so,

MP of AC = MP of BD

$\huge \rightarrow \frac{x + 1}{2},\frac{y+ 3}{2} = \frac{5 + 1}{2},\frac{3 - 2}{2} \\$

$\huge \rightarrow \: x = 5 \: \\ \huge \rightarrow \: y = - 2$

3 0

3 years ago