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GaryK [48]
3 years ago
5

The number of users on a website has grown exponentially since its launch. After 2 months, there were 90 users. After 4 months,

there were 810 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Mathematics
1 answer:
grigory [225]3 years ago
8 0

Answer:

10(3)^x

Step-by-step explanation:

The function contains the points (2,90) and (4,810). Use the general form y=abx to write two equations:

90=ab^2 and 810=ab^4

Solve each equation for a:

a=90/b^2 and a=810/b^4

Since a=a, set the other sides of the equations equal and solve for b.

90/b2=810/b4

Cross multiply, then divide and simplify as follows:

90b^4=810b^2

b^4/b^2=810/90

b^2=90

b^3

Now, use the value of b and the point (2,90) to find the value of a.

90=a(3^2)

a=10

So, substitute answers in original equation for a final answer of f(x)=10(3)^x.

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Solve the equation. <br><br> 2.2= z - 1.1 <br> z=?
fredd [130]

Answer:

z = 3.3

Step-by-step explanation:

Given

2.2 = z - 1.1 ( add 1.1 to both sides )

3.3 = z

7 0
2 years ago
The perimeter of a rectangle is 338, if the ratio of the length to the width is 8:5, find the length
STALIN [3.7K]
Let the length be 8x and the width = 5x, then
Perimeter = 2(length + width) = 2(8x + 5x) = 2(13x) = 26x
338 = 26x
x = 338/26 = 13

Therefore, length = 8x = 8 x 13 = 104
4 0
3 years ago
A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest
nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate          you need to divide by 100 to get it in decimal form

t = time, in years        if you are given a partial year, divide the months by 12

P = $12,000                                    

r = 7.5% = .075                                    

t = 1                                                  

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075        Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0
3 years ago
Robert plans to make a box-and-whisker plot of the following set of data. 27, 14, 46, 38, 32, 18, 21 Which of the following shou
Simora [160]
To make a box and whisker plot, you need to draw a number line that would be able to represent all the values in the data (look at your lowest and highest numbers).

You will need to graph the following 5 points on your number line (median, lower quartile, lower extreme, upper quartile, and upper extreme).

Create a box around the quartiles and extend the lines to the extremes.
See the picture I have attached for the box and whisker box for this data set.

7 0
2 years ago
Rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Olegator [25]

Answer:

36 units²

Step-by-step explanation:

rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?

Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

we use the inverse formula

12 * 3 =<em> </em>

<em>36 units²</em>

<em>-----------------------</em>

check

36 : 12 = 3

the answer is good

7 0
1 year ago
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