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2 years ago

Write an equation for the exponential function represented in the table and graph below.

Mathematics

1 answer:

k0ka [10]2 years ago

8 0

Given:

Given that the values of x and y in the table.

We need to determine the equation for the exponential function represented in the table and graph the equation.

Equation for the exponential function:

The general equation for the exponential function is given by

$y=a(b)^x$ ------- (1)

Substituting the coordinate (0,6) in equation (1), we get;

$6=a(b)^0$

$6=a$

Thus, the value of a is 6.

Substituting a = 6 in equation (1), we have;

$y=6(b)^x$ -------- (2)

Substituting the coordinate (1,12) in equation (2), we get;

$12=6(b)^1$

$12=6b$

$2=b$

Thus, the value of b is 2.

Substituting b = 2 in equation (2), we get;

$y=6(2)^x$

Thus, the equation for the exponential function is $y=6(2)^x$

The image of the graph of the exponential function is attached below:

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Let f(x) = x^2 + 6x.

rusak2 [61]

Answer:

(A) The slope of secant line is 18.

(B) The slope of secant line is h+16.

Step-by-step explanation:

(A)

The given function is

$f(x)=x^2+6x$

At x=3,

$f(3)=(3)^2+6(3)=27$

At x=9,

$f(9)=(9)^2+6(9)=135$

The secant line joining (3,27) and (9,135). So, the slope of secant line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{135-27}{9-3}=18$

The slope of secant line is 18.

(B)

The given function is

$f(x)=x^2+6x$

At x=5,

$f(5)=(5)^2+6(5)=55$

At x=5+h,

$f(5+h)=(5+h)^2+6(5+h)=h^2 + 16 h + 55$

The secant line joining (5,55) and $(5+h,h^2 + 16 h + 55)$ . So, the slope of secant line is

$m=\dfrac{h^2 + 16 h + 55-55}{5+h-5}$

$m=\dfrac{h^2 + 16 h }{h}$

$m=h+16$

The slope of secant line is h+16.

4 0

3 years ago

Quadratic Equation

Natasha_Volkova [10]

Step-by-step explanation:

The sum of ages of two friends is 13 years.

The product of their ages is 42.

Let the age of 1st friend and 2nd friend is x, y respectively.

1 st condition= The sum of ages of two friends is 13 yrs.

i.e x+y = 13........ (I)

2nd condition= The product of their ages is 42.

i.e X*y = 42........(ii)

From equation (I)

X+y = 13

or, X = 13-y........ (iii)

Putting the equation (iii) in equation (ii).

X*y= 42

(13-y) * y = 42

13y - y^2 = 42

${y}^{2} - 13y + 42 = 0$

${y}^{2} - (7 + 6)y + 42= 0$

${y}^{2} - 7y - 6y + 42 = 0$

$y(y - 7) - 6(y - 7) = 0$

$(y - 6) (y - 7) = 0$

Either; y-6 = 0

y = 6

Or;

y-7=0

y = 7

Keeping the value of y as "7" in equation (ii)

x*y = 42

7x = 42

X = 42/7

Therefore, the value of X is 6.

Therefore, either 1st friend is 6 years and 2nd is 7 years.

Hope it helps...

7 0

2 years ago

Tomas works as an underwater photographer. He starts at a position that is 13 feet below sea level. He rises 6 feet, then descen

dangina [55]

Think of sea level as 0 on number line

-13 + 6 - 15

6 0

3 years ago

Suppose you discover that your growth fund, income fund, and money market fund return

Alik [6]

Answer:−3+3=−4

2+3−=15

4−3−=19

2 3

Step 1: Pair the equations to eliminate y because the y terms are already additive inverses

−3+3=−4

2+3−=15

4−3−=19

2 3 4

3 =11

6 −2=34

Step 2: Write the two new equations

as a system

Step 3: Substitute the value for x and z

into one of the original equations

3 =11

3 5 +2=11

5−3+3 −2 =−4

15+2=11

6 −2=34

5−3−6=−4

−3−1=−4

2=−4

=−2

= 45

x = 5

−3=−3

The solution (5, 1, -2)

Step-by-step explanation:

3 0

3 years ago

4x-7x=13 in a fraction

Naddika [18.5K]

4x-7x= 13
⇒ -3x= 13
⇒ x= 13/(-3)
⇒ x= -13/3

The final answer is x= -13/3~

4 0

3 years ago