Determine if the table shows a linear or an exponential function​

2 answers
Question:

Determine if the table shows a linear or an exponential function​

Answers

Answer:The table shows an exponential functionStep-by-step explanation:Linear vs Exponential FunctionsA linear function is written as:[tex]y=mx+b[/tex]where m and b are constants.If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.The slope can be calculated as:[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]An exponential function is written as:[tex]y=y_o.r^x[/tex]Where r is the ratio and yo is a constant.If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.The ratio can be calculated as:[tex]\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}[/tex]Calculate the slope for (0,4) and (1,2):[tex]\displaystyle m=\frac{2-4}{1-0}=-2[/tex]Calculate the slope for (1,2) and (2,1):[tex]\displaystyle m=\frac{1-2}{2-1}=-1[/tex]Since the slope is not the same, the function is not linear. Now calculate the ratio for (0,4) and (1,2)[tex]\displaystyle r=\sqrt[1-0]{\frac{1}{2}}[/tex]The radical of index 1 is simply equal to its argument:[tex]\displaystyle r=\frac{1}{2}[/tex]Now calculate the ratio for (0,4) and (2,1)[tex]\displaystyle r=\sqrt[2-0]{\frac{1}{4}}[/tex][tex]\displaystyle r=\sqrt{\frac{1}{4}}[/tex][tex]\displaystyle r=\frac{1}{2}[/tex]Testing other points we'll find the same ratio, thus the table is an exponential function

Like ya cuttt g..........

Similar Solved Questions

2 answers

The first compact microwave ovens were sold in 1960. Everybody didn’t use them until the 1980’s.a. comma b. and c. or d. but e. because which one would best suit the sentence structure

The first compact microwave ovens were sold in 1960. Everybody didn’t use them until the 1980’s.a. comma b. and c. or d. but e. because which one would best suit the sentence structure...
1 answer

The Mohorovicic discontinuity represents

The Mohorovicic discontinuity represents...
1 answer

A bike moves 50 meters in 5 seconds. Calculate the speed of the bike.

A bike moves 50 meters in 5 seconds. Calculate the speed of the bike....
1 answer

If the radius of the window is 1 foot​, what is the area of the​ glass?

If the radius of the window is 1 foot​, what is the area of the​ glass?...
2 answers

The system of racial segregation in the US South that lasted from 1890 to 1965 was referred to as

The system of racial segregation in the US South that lasted from 1890 to 1965 was referred to as...
1 answer

Erving Goffman coined the term ___________ for the strategies we use to rescue our performance when we experience a potentially or actually embarrassing situation.

Erving Goffman coined the term ___________ for the strategies we use to rescue our performance when we experience a potentially or actually embarrassing situation....
1 answer

A company buys a new bulldozer for $116050. The company depreciates the bulldozer linearly over its useful life of 20 years. Its salvage value at the end of 20 years is $10050. Depreciation is the decrease or loss in value of the equipment due to age, wear, or market conditions. A) Express the value of the bulldozer, V, as a function of how many years old it is, t. B) The value of the bulldozer after 8 years is $ PLEASE HELP ASAP

A company buys a new bulldozer for $116050. The company depreciates the bulldozer linearly over its useful life of 20 years. Its salvage value at the end of 20 years is $10050. Depreciation is the decrease or loss in value of the equipment due to age, wear, or market conditions. A) Express the value...
1 answer

Can anyone please help me

Can anyone please help me...
1 answer

A stress test was found to actually measure sleep deprivation. the stress test would lack:

A stress test was found to actually measure sleep deprivation. the stress test would lack:...
1 answer

How was Santa Anna defeated by the Texans? A. At the battle of the Alamo, he was captured and forced to surrender. B. A surprise attack at Goliad left his army defeated. C. San Antonio was the sight of the most horrible battle and tremendous loss of life for Santa Anna’s army forcing him to turn over his army. D. With help from American supplies, the Texans routed the Mexicans at San Jacinto.

How was Santa Anna defeated by the Texans? A. At the battle of the Alamo, he was captured and forced to surrender. B. A surprise attack at Goliad left his army defeated. C. San Antonio was the sight of the most horrible battle and tremendous loss of life for Santa Anna’s army forcing him to turn...
2 answers

What is the name of the collection of bones that run down your back?

What is the name of the collection of bones that run down your back?...
2 answers

Someone help me Solve x

Someone help me Solve x...
1 answer

Compare these two numbers which one has a greater value 8.5 x 10^23 or 9.99 x 10^21

Compare these two numbers which one has a greater value 8.5 x 10^23 or 9.99 x 10^21...
1 answer

Use division to find all the whole number ratio equivalent to 56:24

Use division to find all the whole number ratio equivalent to 56:24...
2 answers

You and your friend skate at the same rate. You complete 5 laps in 7 minutes. How long does your friend take to complete 15 laps? Just the NUMBER PLEASE I NEED THIS ANSWER ASAP PLEASE HURRY ILL GIVE BRAINLY

You and your friend skate at the same rate. You complete 5 laps in 7 minutes. How long does your friend take to complete 15 laps? Just the NUMBER PLEASE I NEED THIS ANSWER ASAP PLEASE HURRY ILL GIVE BRAINLY...
1 answer

Multiple choice ?? We use iron rods as our money Monarchy Athens Democracy Sparta

Multiple choice ?? We use iron rods as our money Monarchy Athens Democracy Sparta...
1 answer

1. Infer The narrator uses many idioms, commonly-used expressions that mean something other than the literal meaning of their words. For example, when Juan is "caught ... with his guard down," the author means that he wasn't being cautious, not that he physically protected himself most of the time. What tone, or attitude toward the character and the audience, do the idioms create?

1. Infer The narrator uses many idioms, commonly-used expressions that mean something other than the literal meaning of their words. For example, when Juan is "caught ... with his guard down," the author means that he wasn't being cautious, not that he physically protected himself most of the time. ...
1 answer

Find the gradients of lines A and B. B YA 14 112 8 6 4 2 -3 -2 -12 Х $ od

Find the gradients of lines A and B. B YA 14 112 8 6 4 2 -3 -2 -12 Х $ od...
1 answer

Una compañía de danza de 156 bailarines hace una coreografía formando filas y columnas.Si en una fila hay 20 bailarines más que en una columna ¿cuántas filas y cuantas columnas son?

Una compañía de danza de 156 bailarines hace una coreografía formando filas y columnas.Si en una fila hay 20 bailarines más que en una columna ¿cuántas filas y cuantas columnas son?...
2 answers

20 POINTS please help

20 POINTS please help...

-- 0.036848--