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Oksana_A [137]
3 years ago
14

The graph of an exponential function passes through the point (0,15) and (1,10). What is the equation of the exponential functio

n that models the curve that passes through these two points? Explain your answer using complete sentences.

Mathematics
1 answer:
Vilka [71]3 years ago
7 0

Answer:

y=15(\frac{2}{3})^x

Step-by-step explanation:

we know that

The equation of a exponential function is of the form

y=a(b^x)

where

a is the initial value or y-intercept

b is the base of the exponential function

In this problem we have

a=15 ----> the y-intercept is given

substitute

y=15(b^x)

we have the other ordered pair (1,10)

substitute the value of x and the value of y and solve for b

10=15(b^1)\\10=15b

b=\frac{10}{15}=\frac{2}{3}

substitute

y=15(\frac{2}{3})^x

see the attached figure to better understand the problem

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How do i find the shorted distance between the point and the line
m_a_m_a [10]

Answer:

5 units

Step-by-step explanation:

3x + 4y = 8

4y = -3x+8

y = -3/4+2

The shortest distance between a point and a line is the perpendicular line.

Slope of the perpendicular line: 4/3 and point (-3,-2)

b = -2-(4/3)(-3) = 2

Equation of the perpendicular line: y=4/3x+2

y is equal y

4/3x+2= -3/4x+2

4/3x +3/4x = 2-2

x = 0

Plug x=0 into one of the equations to find y

y = 4/3(0) + 2

y = 2

(0,2) and (-3,-2)

Distance = sqrt [(-3-0)^2 + (-2-2)^2]

Sqrt (-3)^2+ (-4)^2

Sqrt 25 = 5

3 0
2 years ago
Assuming a 90% confidence level, the margin of error is approximately?
elena-s [515]

Answer:

  0.3

Step-by-step explanation:

The margin of error is calculated as ...

  (standard deviation)/√(sample size) × (z*-score)

where the z*-score is chosen based on the desired confidence level.

Here, you have ...

  • standard deviation = 2.7
  • √(sample size) = √225 = 15
  • z*-score for 90% confidence level = 1.645

Putting these values in the above expression for margin of error gives ...

  2.7/15·1.645 = 0.2961 ≈ 0.3

7 0
3 years ago
Find the values of x that satisfy
mr_godi [17]
Setup 2 problems
2x - 7 < 15   and    2x - 7 > -15
2x < 22                  2x > -8
x < 11                    x > -4

Or you can write it  -4 < x < 11

7 0
3 years ago
By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
Vadim26 [7]
The Boat Turned 39 Degrees
6 0
3 years ago
Read 2 more answers
A first number plus twice a second number is 11. Twice the first number plus the second totals 16. Find the numbers.
satela [25.4K]
<h3><u>The first number, x, is equal to 7.</u></h3><h3><u>The second number, y, is equal to 2.</u></h3>

x + 2y = 11

2x + y = 16

We can subtract 2y from both sides of the first equation to get a value for x.

x = 11 - 2y

Because we have a value for x, we can plug it into the second equation.

2(11 - 2y) + y = 16

Distributive property.

22 - 4y + y = 16

Combine like terms.

22 - 3y = 16

Subtract 22 from both sides.

-3y = -6

Divide both sides by -3.

y = 2

Now that we have a value for y, we can plug it into either equation to solve for x.

x + 2(2) = 11

x + 4 = 11

Subtract 4 from both sides.

x = 7



4 0
3 years ago
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