MATHEMATICS HIGH SCHOOL

Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.

Answers

Answer 1

Answer:

The exponential function that models the following situation is given as follows:

$A(t) = 470(0.88)^t$

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem:

The initial population is of 470 animals, hence A(0) = 470.

It decreases 12% a year, hence r = 0.12.

Then, the equation is given by:

$A(t) = A(0)(1 - r)^t$

$A(t) = 470(1 - 0.12)^t$

$A(t) = 470(0.88)^t$

More can be learned about exponential functions at brainly.com/question/25537936

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Answer 2

Answer: $\bf \qquad \textit{Amount for Exponential Decay}\n\nA=P(1 - r)^t\qquad \begin{cases}A=\textit{accumulated amount}\nP=\textit{initial amount}\to &470\nr=rate\to 12\%\to (12)/(100)\to &0.12\nt=\textit{elapsed time}\n\end{cases}\n\n\nA=470(1-0.12)^t\implies A=470(0.88)^t$

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8,330,000,000 written in scientific notation?
Solve for m: 18d – 2m + 9k < 5k + 10.

What is the problem of this solving?!

Answers

This question can be solved primarily by L'Hospital Rule and the Product Rule.

$y= \lim_(x \to 0) (x^2cos(x)-sin^2(x))/(x^4)$

I) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([2xcos(x)-x^2sin(x)]-2sin(x)cos(x))/(4x^3)$

II) Product Rule and L'Hospital Rule:

$y= \lim_(x \to 0) ([-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)])/(12x^2) \n y= \lim_(x \to 0) (2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x))/(12x^2)$

III) Product Rule and L'Hospital Rule:

$]y= \alpha + \beta \n \n \alpha =\lim_(x \to 0) (-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)])/(24x) \n \beta = \lim_(x \to 0) (4sin(x)cos(x)+4sin(x)cos(x))/(24x) \n \n y = \lim_(x \to 0) (-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x))/(24x)$

IV) Product Rule and L'Hospital Rule:

$y = \phi + \varphi \n \n \phi = \lim_(x \to 0) (-6cos(x)-[-4xsin(x)+4cos(x)]-[2cos(x)-2xsin(x)])/(24x) \n \varphi = \lim_(x \to 0) ([2xsin(x)+x^2cos(x)]+[8cos^2(x)-8sin(x)])/(24x)$

V) Using the Definition of Limit:

$y= (-6*1-4*1-2*1+8*1^2)/(24) \n y= (-4)/(24) \n \boxed {y= (-1)/(6) }$

I need help i honestly don’t understand.

Answers

Answer:

basically she earns 800 regardless of whatever happens, and depending on how much she sells we give her 12% of that

so just take the value on the left and multiple by .12 and add to 800

not sure what the 5000 is

hope this helps

What is the measure of AC?
Enter your answer in the box. Enter only the numerical value.

Answers

Step-by-step explanation:

Angle BDC is an angle inscribed in a circle. As such it intercepts TWICE as many degrees of arc as its measure

so: 2 * (3x-1.5) = 3x+9

6x -3 = 3x+9

x = 4

then the arc AC = 3x+9 = 21 degrees

3 1/4 divided by 2 2/3
Please answer and then explain.

Answers

Hello,
If there is a methode for dividing mixed numbers, i would like to see it

For me, european, 3&1/4=13/4
2&2/3=8/3
(13/4)/(8/3)=13/4*3/8=39/32=1&7/32

The area of circle b is 36 times greater than the area of circle a. the radius of circle b is 30. what is the radius of circle a?

Answers

The radius of circle a is 5

Let, area of circle a = a and of b = b

A.T.Q,

36a = b

36a = 30

a = 30/36 = 5/6

πr² = 5/6

r² = 5/6π

r = √5/√6π

You can calculate that further by putting the value of π

What are the domain and range of the relation given in the table?

Answers

Answer:

Step-by-step explanation:

all x values is domain, all y values are range

Answer:

Its c

Step-by-step explanation:

Domain = x value

Range = y value

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