write an exponential function y=ab^x for a graph that includes (2,4) and (3,16)

Answer:

Using the equation y = abx , substitute both of your given points into that equation.

 2 = ab2 and 4 = ab3   Solve each equation for a.

 2⁄b2    and 4⁄b3 = a    

Therefore, 2⁄b2 = 4⁄b3

Cross multiply: 2b3 = 4b2    

Divide both sides by b2

 2b = 4      

a = 2/4 = 1/2

b = 2

 y = 1 (2)x

2

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9514 1404 393

Answer:

  y = (1/4)4^x

Step-by-step explanation:

In general, you can use a 2-point form to write the exponential function for points (x1, y1) and (x2, y2) as ...

  y = y1·(y2/y1)^((x -x1)/(x2 -x1))

Using the given points, this becomes ...

  y = 4·(16/4)^((x -2)/(3 -2)) = 4·4^(x-2)

We can eliminate the exponent arithmetic by making use of a couple of rules of exponents.

  y = 4·(4^x)(4^-2) = (4^-1)(4^x)

  y = (1/4)(4^x)

Please help ASAP!!!!

A jar contains 666 red jelly beans, 666 green jelly beans, and 666 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be green and the second will be green as well?

Find the slope of the line.

so its 8p = 56 is the frist bit and the second is 7. BOOM

Given the balanced equation representing a reaction:

2H2 + O2 > 2H2O

The oxidation state of hydrogen in this reaction changes from

A)
–1 to +1

B)
–1 to +5

C)
0 to +1

D)
+5 to –1

Can someone please help meee

Q1: A number minus 4 is greater than 2 times a number

What is the next term in the following sequence?

54, -18, 6, ...

-2
3
2
-3

A cyclist starts from the point si = (7, 7, 4) at t = 0 and moves with a constant velocity of v → =(4, 5, 5) and cyclist motion can be depicted by the expression, s = si + vt which gives position vector of cyclist. Determine the distance travelled by the cyclist between t = 4 s and t = 23 s. (Distance is in meters)
A. 154.36 m
B. 157.36 m
C. 152.36 m
D. 155.36 m

Find the solutions for 6x^2 -7x-20=0

Angie has 3 pink bows, 1 blue bow, and 6 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Angie will choose a purple bow?

Shawna went shopping at the thrift store yesterday and came home with 12 items and she only spent $31.50. She only got shirts and pants. If each shirt cost $2 and each pair of pants cost $3.50, which system of equations would represent this situation?

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30. A car's value is a function of many things,
including the total mileage on the car. The
following graph illustrates the depreciation of a
car as more miles are driven. Find the value of
f(50,000) and explain its meaning. What is the
range of this function?
Car's valde
$14,000
$12,000
$10,000
$8.000
$6,000
$4,000
$2,000
$0
20,000 40.000 60.000 80.000 100.000 120,000
Mileage

1 half of 4 over 5 = ____ fifth(s)

What is the slope of the line perpendicular to
y=3x-12

What is the average of 100, 54 and 88?

A label that wraps around a box of golf balls covers 75 percent of its lateral surface area. What is the value of x?

Can somebody help me?

Need help ASAP please!

Which expression is equivalent to b less than 50?
A 50b
B b - 50
C 50/b
D 50 - b

Write the pair of fractions as a pair of fractions with
common denominator
1/2 and 1/3

A roulette wheel consists of 18 red slots, 18 black slots, and 2 green slots. A player can wager $1 that a marble will land in a red slot, in which case the player would gain a $1. If the marble lands in a slot that isn't red, then the player loses their $1 wager. Let X represent the player's gain from a random $1 wager on red. Here's the probability distribution of X along with summary statistics:
Lose Win
X = gain (S) -1 1
Р(X) 20/38 18/38
Мean: Ax-$0.05
Standard deviation: ax$1.00
Suppose a player decides to wager $5 instead of winning $5.
Let Z represent the player's gain from a random $5 wager on red. possible outcomes become either losing or , so
What are the mean and standard deviation of Z? dollars?

HELP HELP HELPPPP SOMEONE PLEASE-

In a poll of students at the hockey championship, 87% of the students say that hockey is better than baseball.
(a) Explain why it is not a valid conclusion to say that hockey is more popular than baseball at the school.

what is the value of 4/15 divide 2/3

Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)

potrzebuję na teraz pls

7. Simplify
(12p27
(2p2q6)​

FIRST TO ANSWER GETS BRAINLIEST!!!
Find the y-intercept of the following line:
y=−8x+7

Data represented by quantities is called data.