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vladimir2022 [97]
2 years ago
11

NO LINKS!! Explain your answers (show the support by showing the changes in x and y on your table). If the relationship is linea

r, inverse, or exponential, write the equation.
#5 and #6​

Mathematics
1 answer:
sdas [7]2 years ago
5 0

Answer:

<u>Linear relationship</u>: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.

<u>Inverse relationship</u>:  the value of one variable decreases as the value of the other variable increases.

<u>Exponential relationship</u>: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)

<u>Question 5</u>

As the x-value increases (by one unit), the y-value decreases.

Therefore, this is an inverse relationship.

The y-values are calculated by dividing 35 by the x-value.

\sf y=\dfrac{35}{x}

**I believe there is a typing error in the table and that the y-value of x = 3 should be 11.67**

<u>Question 6</u>

As the x-value increases, the y-value increases.  The y-value increases by a factor of 5 for each x-value increase of 1 unit.

Therefore, this is an exponential relationship.

\sf y=5^x

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A candle on pauline’s dresser is 10 inches tall and burns at a rate of 0.75 inches per hour. how many hours will it take for the
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Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

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