5. What is the slope of the line whose equation is

Which of the following situations could be modeled by an exponential function?

Sauron [17]

Answer: Option D.

Step-by-step explanation:

An exponential function is something like:

f(x) = A*(r)^x

Where:

A = initial amount.

r = rate of growth

x = variable.

This type of function is used to describe situations like "you have A dollars, and it increases by 30% each week"

or:

"There is a population of A animals, and it doubles each year"

Let's analyze briefly all the given options and see which one is an exponential function.

A) The water level of a tank decreases by 5 gallons every day.

This is a linear relation, if W is the initial amount of water, and x is the number of days, then the water level of the tank after x days is:

y = W - 5 gal*x

B) The amount of money collected by a charity increases by $5,000 each year.

The amount collected increases $5000 each year.

Then if in year 1 they collected A.

in year 2 they collected A + $5000

in year 3 they collected A + 2*$5000

We already can see the pattern, this is a linear relation:

in year X they colected A + (X - 1)*$5000

C) A tree was 10 feet tall when purchased and grows at a rate of 2 feet per year.

if y is the height of the tree, and x is the number of years, this can be written as:

y = 10ft + x*2ft

Again, a linear relation.

D) The number of people in a stadium is decreasing at a rate of 45% every 10 minutes.

Let's define x as each "lapse" of 10 minutes that passes.

If N is the initial number of people in te stadium, then after 10 minutes the number of people is = N*(1 - 45%/100%) = N*(1 - 0.45) = N*0.55

After another 10 minutes, the population decreases again.

N*0.55*(1 - 45%/100%) = N*0.55*0.55 = N*0.55^2

We can see the pattern here, this can be written as

People(x) = N*(0.55)^x

This is an exponential function.

3 0

3 years ago

there are 36 members in an investment club. the number of 40% of the males in the club is equal to 50% of the number of females.

Alborosie

Answer:

Their is 10% of males and females.

Step-by-step explanation:

Because if you subtract 50% and 40%you would get 10% that means their is more females.

3 0

3 years ago

Read 2 more answers

how many pounds of 2/3 pound burger would you need to eat to consume the equivalent of the 360 pound burger

Zina [86]

360÷2/3=

360×3/2 = 1080/2

1080/2 = 540

540 burgers

8 0

3 years ago

Tom made a vegetable pizza and a pepperoni pizza. he cut the vegetable pizza into 5 slices and the pepperoni pizza into 10 equal

Anon25 [30]

I may not be the best at this but I believe that Tom’s friends ate the same amount of pepperoni pizza to vegetable pizza because He cut the pizza into 5 slices as to the pepperoni into 10 slices is. The fraction of Vegetable to Pepperoni is 1/2 so 2 vegetable slices is the same amount as 4 slices because the pepperoni pizza is in smaller sizes compared to the Vegetable pizza.

5 0

3 years ago

Read 2 more answers

farmer ryan has corn field that is nearly a rectangle. the length is five meters more than the width. the perimeter is about 210

Tcecarenko [31]

Farmer ryan has a corn feild that is in the shape of a rectangle. The length is five meters more than the width. The perimeter is 210 meters.

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Question 1123428: A bucket is in the shape of a truncated cone.The height of the bucket is 45 cm,and the diameters of the top and the bottom surfaces are 56 cm and 14 cm respectively.Find the the quantity (in litres) of the water the bucket can hold.

Answer by Boreal(9049) About Me (Show Source):

You can put this solution on YOUR website!

V=(1/3)(r1^2+r1r2+r2^2)h*pi

=(1/3)*45*(28^2+196+49)*pi

=15(1029)*pi

A piece of paper is in the shape of a sector of a circle whose radius is 12 cm and the central angle of the sector is 120 degree.

It is rolled to form a cone of the biggest possible capacity.

Find the capacity of cone.

:

Find the total area of the sector

A = 120%2F360*pi%2A12%5E2

A = 150.8 sq/cm, this is surface area of the cone

:

Surface area (SA) of a cone without the end formula

The slant length (s) = the radius of the paper; 12 cm

pi%2Ar%2As+=+SA

pi%2Ar%2A12+=+150.8 , find r, the radius of the cone

r = 150.8%2F%2812%2Api%29

r = 4 cm is the radius

find the height of the cone

h = sqrt%28s%5E2-r%5E2%29

h = sqrt%2812%5E2-4%5E2%29

h = 11.3 cm is the height of the cone

Find the capacity (volume)

V+=+1%2F3*+pi%2Ar%5E2%2Ah

V = 1%2F3*pi%2A4%5E2%2A11.3

V = 189.33 cu/cm

6 0

3 years ago