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1 year ago

What is the range of the exponential function shown below

Mathematics

2 answers:

kvv77 [185]1 year ago

6 0

Answer:

The correct option is C.

Step-by-step explanation:

Range is the set of output or the values of the function.

The given function is

$f(x)=9\cdot 2^x$

If a exponential function is defined as g(x)=a^x, where a>0, then the value of g(x) is always greater than 0, g(x)>0.

It means,

$2^x>0$

Multiply both sides by 9.

$9\cdot 2^x>9\cdot 0$

$9\cdot 2^x>0$

$f(x)>0$

The value of the function f(x) is always greater than 0, therefore the range of the function is

Range = { y | y>0}

Hence the correct option is C.

Vsevolod [243]1 year ago

3 0

Answer : y>0

f(x) = 9*2^x

f(x) is an exponential function

$f(x) = 9*2^x$

When we plug in positive value for x , the value of y is positive

When we plug in negative value for x , the value y is also positive

So for any value of x, the y value is positive always.

Range is the set of y values for which the function is defined

y values are positive , so range is y >0

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Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard de

hammer [34]

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

4 0

2 years ago

A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s

kondaur [170]

Hello,

g=9.81m/s²= 9.81/0.3048 =32.18.. ft/s² rounded to 32

h=-g/2*t²+vt+h0
if t=0,h=0 ==>h0=0

==>h=-16*t²+vt
50 ft in 2.5s ==> 25 ft in 1.25s

25=-16*1.25²+v*1.25
==>v=50/1.25=40

Equation h=-16t²+40*t

6 0

1 year ago

You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At F

julia-pushkina [17]

Answer:

B. Food market

Step-by-step explanation:

You typically buy all of your groceries at Grocery Mart. This week, your favorite cereal is on sale there, 4 boxes for $10. At Food Market, where you don’t typically shop, the same cereal is on sale for $2.25 a box. Based on price, which is the better value option?

A.Grocery Mart

B. Food Market

Grocery market:

4 boxes for $10

Unit price = cost / quantity

= $10 / 4 boxes

= $2.50 per box

Food market:

Price per box = $2.25

The better value option based on price is food market because it cost less to buy a box of cereal than grocery mart

8 0

1 year ago

A man starts at the point O on the map below. He chooses a path at random and follows it to point B1, B2, or B3. From that point

natita [175]

Answer: 1 / 27

Step-by-step explanation: p (B1) = 1 / 3

p (B2) = 1 / 3

p (B3) = 1 / 3

pro (B1 X B2 X B3) = 1 / 3 X 1 / 3 X 1 / 3 = 1 / 27

6 0

1 year ago

A tank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then

stellarik [79]

Let $A(t)$ be the amount of salt in the tank at time $t$ . We're given that $A(0)=40$ . The rate at which this amount changes is given by

$A'(t)=\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{4\text{ oz}}{1\text{ gal}}-\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ oz}}{100+(5-5)t\text{ gal}}$

$A'(t)+\dfrac{A(t)}{20}=20$

$e^{t/20}A'(t)+e^{t/20}\dfrac{A(t)}{20}=20e^{t/20}$

$\bigg(e^{t/20}A(t)\bigg)'=20e^{t/20}$

$e^{t/20}A(t)=400e^{t/20}+C$

$A(t)=400+Ce^{-t/20}$

Since $A(0)=40$ , we get

$40=400+C\implies C=-360$

so that the amount of salt at time $t$ is

$A(t)=400-360e^{-t/20}$

After 20 minutes, the tank contains

$A(20)=400-360e^{-20/20}\approx267.56\text{ oz}$

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1 year ago