All categories

3 years ago

Frogs are released into a pond where there are no other frogs of this species. The

Mathematics

1 answer:

ivolga24 [154]3 years ago

3 0

Answer:

$f(t)=12(1.0139)^{12t}$

Step-by-step explanation:

Let the initial number of frogs = 12

And their population is growing with the annual growth rate = 16.68% per year

Function modeling the population after 't' years will be,

$P(t)=12(1+r)^{t}$

Here, r = Annual growth rate

t = Number of years

If we convert the annual growth rate to monthly growth rate,

Expression modeling the population will be,

$f(t)=12(1+\frac{r}{12})^{12t}$

$=12(1+\frac{16.68}{12})^{12t}$

$=12(1.0139)^{12t}$

Therefore, $f(t)=12(1.0139)^{12t}$ will be the answer.

You might be interested in

Someone help (find the inverse)

Yanka [14]

The value of inverse function when x = 0 is 1, when x = 1 is infinity or not defined, and when x = 3 is -1/2.

What is function?

A function in mathematics is an expression, rule, or law that determines the relationship between two variables, one of which is independent, and the other of which is dependent (the dependent variable). The traditional notion of function was first proposed by German mathematician Peter Dirichlet in 1837.

The function for the line shown in the graph can be written as:

y = -x + 1

Here, y = f(x)

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

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

We can put the given values in place of x in this function:

$f^{-1}(0) = 1$

$f^{-1}(1) = infinity$ or ( not defined)

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

This is the required answers.

To know more about functions, go to link

brainly.com/question/10439235

#SPJ13

7 0

1 year ago

Determine whether each function has an inverse function. If it does, find the inverse function and state any restrictions on its

Talja [164]

QUESTION 1

The given function is;

$f(x) = |x - 6|$

This is an absolute value function.

For this function to have an inverse it must be a one-to-one function.

This absolute value function is not one-to-one
because

$f( 5)=1$
and

$f(7) = 1$

Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.

You can see from the graph that this function cannot pass the horizontal line test.

QUESTION 2

The given function is

$f(x) = \sqrt{6 - {x}^{2} }$

Let

$y= \sqrt{6 - {x}^{2} }$

This implies that,

${y}^{2} + {x}^{2} = 6$

We see clearly that, this function is a circle that is centered at the origin.

This means that,

$f(x) = \sqrt{6 - {x}^{2} }$

is a semicircle.

This function will not pass the horizontal line test and hence does not have an inverse.

QUESTION 3

The given function is

$h(x) = \frac{x+4}{3x-5}$

If we put

$h(a) = h(b)$

We obtain,

$\frac{a+4}{3a-5} = \frac{b+4}{3b-5}$

$(a + 4)(3b - 5) = (b + 4)(3a - 5)$

$3ab - 5a + 12b - 20 = 3ab - 5b + 12a - 20$

$- 17a = - 17b$

$a = b$

This shows that h(x) has an inverse because it is one-to-one.

Let

$y=\frac{x+4}{3x-5}$

We interchange x and y to get,

$x=\frac{y+4}{3y-5}$

$x(3y - 5) = y + 4$

$3xy - 5x = y + 4$

Group like terms to get,

$3xy - y = 5x + 4$

Factor to get,

$y(3x - 1) = 5x + 4$
Solve for y,

$y = \frac{5x + 4}{3x - 1}$

Hence

${f}^{ - 1}(x) = \frac{5x + 4}{3x - 1}$

where

$x \ne \frac{1}{3}$

6 0

3 years ago

A lumber company is making boards that are 2701.0

Harlamova29_29 [7]

Good for u are u gonna help them like there's not even a question there u bozo

7 0

3 years ago

the price opf a 3 pack of Spinners is one third the price of a dozen Fly Boys what is the price of a dozen Fly Boys?

miss Akunina [59]

You have to be more specific (what is the cost?)

7 0

4 years ago

What is the remainder in the synthetic division problem below?

Naddik [55]

Answer:

The remainder is 25 ⇒ answer (C)

Step-by-step explanation:

* The remainder will be the last number in the calculation

* From the picture the dividend is 3x³ + x² + 2x - 7 and x - 2 is the divisor

- In the synthetic calculation we use the coefficient of the dividend with the value of x when the divisor = 0

- From the picture the divisor is x - 2, when x - 2 = 0, then x = 2

∵ The coefficient of the dividend are 3 , 1 , 2 , -7

Step 1 : Write down the coefficients of the dividend , put x = 2 at the left

2 3 1 2 -7

_____________

Step 2 : Bring down the first coefficient to the bottom row.

2 3 1 2 -7

____________

Step 3 : Multiply it by 2, and carry the result into the next column.

2 3 1 2 -7

___6_________

Step 4 : Add down the column

2 3 1 2 -7

___6_________

3 7

Step 5 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_______

3 7

Step 6 : Add down the column

2 3 1 2 -7

___6_14_______

3 7 16

Step 7 : Multiply it by 2, and carry the result into the next column

2 3 1 2 -7

___6_14_32______

3 7 16

Step 8 : Add down the column

2 3 1 2 -7

___6_14_32______

3 7 16 25

∴ The quotient is (3x² + 7x + 16) and the remainder is 25

6 0

3 years ago

Read 2 more answers