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3 years ago

Write an exponential function to model the situation.A population of 300 animals decreased at an annual rate of 22%

Mathematics

1 answer:

erastovalidia [21]3 years ago

4 0

Answer:

$y = 300(0.78)^x$

Step-by-step explanation:

x is the number of years. y is the population after x years.

Each year, the population decreases by 22%, since 100% - 22% = 78%, and 78% = 0.78, each year, the population is 0.78 of the previous year's population.

year zero: y = 300

year 1: y = 300 * 0.78 = 300 * (0.78)^1

year 2: y = (300 * 0.78) * 0.78 = 300 * (0.78)^2

year 3: y = ((300 * 0.78) * 0.78) * 0.78 = 300 * (0.78)^3

year x: y = 300(0.78)^x

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A circular window is drawn on architectural plans where each unit is a foot on a coordinate grid. the window is modeled by the e

Pie

The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

<h3>What is the general equation of a circle?</h3>

The equation of a circle is given by the formula,

$(x-a)^{2} + (y -b)^{2} = r^{2}$

where (a,b) is the coordinate of the center of the circle, and r is the radius of the circle.

According to the given equation, if we compare this equation with the general equation of the circle.

$(x-4)^{2} + (y-12)^{2} = 9$

$(x-a)^{2} + (y -b)^{2} = r^{2}$

$(x-4)^{2} + (y -9)^{2} = 3^{2}$

On observing this equation we will get that the value of (a,b) is (4,12).

Thus, The equation indicates that the center of the window is 12 feet from the ground

window span = diameter of circle

window span = 2r

= 2 × 3 (radius = 3)

= 6

Hence, The equation indicates that the center of the window is 12 feet from the ground and the distance the window spans 6 feet.

To learn more about Equation of the circle from the given link

brainly.com/question/22223658

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6 0

1 year ago

Gianna put $1000 in a savings account for 18 months, The interest on the account is 3.5%. How much will Gianna earn in interest?

zimovet [89]

Answer:

amount of interest = 52.5

amount at the end of the period = 1052.5

Step-by-step explanation:

use the formula for simple interest

PRT/100

P is the principle

R is the rate of interest charged

T is the Time taken

18 months = 1 years 6 months ( 1.5 years)

1000 * 3.5 * 1.5 = 5250

5250/100 = 52.5

the amount of interest = <u>52.5</u>

the amount she will have at the end of the period

= 1000 +52.5

= <u>1052.5</u>

8 0

3 years ago

If F(x)=3x-2/6 which of the following is the inverse of F(x)?

lana66690 [7]

Answer:

Step-by-step explanation:

I'm seeing that f(x) is

$\frac{3x-2}{6}$

What you do to find an inverse is switch the x and y coordinates and then solve for the new y. Switching the x and y gives us:

$x=\frac{3y-2}{6}$

Now we have to solve for the new y. Begin by muliplying both sides by 6 to get:

6x = 3y - 2 and

6x + 2 = 3y so

2x + 2/3 = y

To put it back into function notation:

$f^{-1}(x)=2x+\frac{2}{3}$

6 0

3 years ago

Midsegment of triangle <br> Find X

Charra [1.4K]

Answer:

$10 = x$

Step-by-step explanation:

This is what is called the Midsegment Theorem, which states that the relation of a triangle's midpunkt is parallel to the triangle's third side, and the mid-segment length is half the third side length, so you would take half of $4x + 20$ and set that expression equal to the midsegment:

2x + 10 = 3x

-2x - 2x

____________

$10 = x$

You then plug this back into both expressions above to get the double-segment of 60 and the mid-segment of 30. We can tell this is correct because 30 and 60 are relatively proportional to each other.

I am joyous to assist you anytime.

4 0

3 years ago

Divide and write in simplest form 2 1/7 divided by 1 1/4

stich3 [128]

Hi!

<h3>To divide a fraction, you multiply by the reciprocal of the second fraction. </h3><h3>First, convert the mixed numbers to fractions, by multiplying the denominator by the whole number and adding that to the numerator. </h3>

---------------

2 * 7 = 14

14 + 1 = 15

15/7

---------------

4 * 1 = 4

4 + 1 = 5

5/4

---------------

<u> $\frac{15}{7} * \frac{4}{5} = \frac{60}{35} (simplify) = 1 \frac{5}{7}$ </u>

<h2>The answer is 1 5/7 </h2>

Hope this helps! :)

-Peredhel

3 0

3 years ago