HELP ME!!! Which of the following expressions is equivalent to 16x2 + 6x + 8?

Determine if the table shows a linear or an exponential function

____ [38]

Answer:

The table shows an exponential function

Step-by-step explanation:

Linear vs Exponential Functions

A linear function is written as:

$y=mx+b$

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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

An exponential function is written as:

$y=y_o.r^x$

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:

$\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}$

Calculate the slope for (0,4) and (1,2):

$\displaystyle m=\frac{2-4}{1-0}=-2$

Calculate the slope for (1,2) and (2,1):

$\displaystyle m=\frac{1-2}{2-1}=-1$

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

$\displaystyle r=\sqrt[1-0]{\frac{1}{2}}$

The radical of index 1 is simply equal to its argument:

$\displaystyle r=\frac{1}{2}$

Now calculate the ratio for (0,4) and (2,1)

$\displaystyle r=\sqrt[2-0]{\frac{1}{4}}$

$\displaystyle r=\sqrt{\frac{1}{4}}$

$\displaystyle r=\frac{1}{2}$

Testing other points we'll find the same ratio, thus the table is an exponential function

4 0

3 years ago

Read 2 more answers

How do you distinguish between multiples and factors of a number, and justify your evaluation of the LCM & GCF of a set of n

Reil [10]

Answer:

Look to the explanation

Step-by-step explanation:

- Multiples of a number are the numbers after multiplying the number

by an integer

- Ex: The multiples of 2 are 2 , 4 , 6 , 8 , .......... because 2 × 1 = 2 ,

2 × 4 = 4 , 2 × 3 = 6 and 2 × 4 = 8

- Factors of a number are the number multiplied together to get the

number

- Ex: The factors of 6 are 1 , 2 , 3 , 6 because 1 × 6 = 6 and 2 × 3 = 6

- Lowest common multiple of the set of numbers (LCM) is the

smallest number divisible by these numbers

- Ex: The lowest common multiple of 2 and 3 is 6 because 6 is divisible

by 2 and 3 and there is no number before it divisible by both

- Greatest common factor of the set of numbers (GCF) is the highest

common factor of these numbers

- Ex: The greatest common factor of 12 and 18 is 6 because

→ The factors of 12 are 1 , 2 , 3, 4, 6, 12

→ The factors of 18 are 1 , 2 , 3 , 6 , 9 , 18

→ The greatest common factor on both numbers is 6

3 0

3 years ago

Please help question in picture!

eduard

Answer:

b

Step-by-step explanation:

6 0

3 years ago

The distance between two cities is 180km. The distance was covered by a car at the rate of 50km/h, by a bus 45km/h, by a truck a

Gennadij [26K]

Answer:

The speed and time are directly proportional in that the higher the speed the lesser the time and vice versa.

The constant is the total distance which is 180 km

Step-by-step explanation:

Step one:

given data

The distance between the two cities is 180km

1.The distance was covered by a car at the rate of 50km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/50

time= 3.6 hours

2.The distance was covered by a bus 45km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/45

time= 4 hours

3.The distance was covered by a bicycle at 25km/h

The time taken will be

velocity= distance/time

time= distance/velocity

time= 180/25

time= 7.2 hours

7 0

3 years ago

J = K (1+ p/100) make p as a subject

olganol [36]

Answer:

p = 100(J/K - 1)

Step-by-step explanation:

When we want to make a variable the subject of an equation, we want to get that variable by itself on one side of the equation - to unwrap it from all the operations attached to it.

Here's what the process looks like for p:

$J=K(1+p/100)\\J/K=1+p/100\\J/K-1=p/100\\p=100(J/K-1)$

8 0

2 years ago