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2 years ago

Please help!!!! For the exponential function...

Mathematics

1 answer:

Anarel [89]2 years ago

4 0

Answer: b.) 40

Given that:

f(x) = 5 × 2ˣ

To find f(3), simplify insert [x = 3] in the given equation:

f(3) = 5 × 2³

f(3) = 5 × 2 × 2 × 2

f(3) = 40

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Plane H is shown which points are viola at and non collinear

enyata [817]

Answer:

I need a picture.

Step-by-step explanation:

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3 0

3 years ago

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

wlad13 [49]

Answer:

$\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

$f(x)=\frac{u(x)}{v(x)}\\$ , the derivative is express as

$\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }$

from $y=lnx/x^{2}$

we assign u(x)=lnx and v(x)=x^2

and the derivatives

$\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\$ .

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e $y=lnx\\\frac{dy}{dx}=\frac{1}{x}$

If we substitute values into the quotient expression we arrive at

$\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

8 0

3 years ago

Do you agree with the researchers method of predicting the population? Why or why not?

Burka [1]

Yes, I agree with the researcher's method. All the values of $a_{n}$ in the table correspond to the values of n by using their formula.

Step-by-step explanation:

Step 1:

If we substitute the values of n in the researcher's equation and we get the right values of $a_{n}$ , we can agree with the researcher's method.

The researcher's formula is $a_{n} = 1000(2)^{n-1}.$ Here $a_{n}$ is the wombat population and n is the number of years.

Step 2:

When n = 1, $a_{1} = 1000(2)^{1-1} = 1000(1) = 1,000,$

when n = 2, $a_{2} = 1000(2)^{2-1} = 1000(2) = 2,000,$

when n = 3, $a_{3} = 1000(2)^{3-1} = 1000(4) = 4,000,$

when n = 4, $a_{4} = 1000(2)^{4-1} = 1000(8) = 8,000,$

when n = 5, $a_{5} = 1000(2)^{5-1} = 1000(16) = 16,000.$

As all the values correspond to the values on the table, I agree with the researcher's method.

6 0

3 years ago

I'm don't understand polygons, as you should know

lawyer [7]

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5, thus

sum = 180° × 3 = 540°

8 0

3 years ago

Read 2 more answers

A bacteria culture contains 1500 bacteria initially and doubles every hour. (a) Find a function N that models the number of bact

Tpy6a [65]

Answer: a) $N(t)=1500(2)^t$

b) 25165824000

Step-by-step explanation:

The exponential equation for growth is given by :-

$y= ab^t$ , where a= initial value , b =multiplicative growth factor and t = time.

Given : A bacteria culture contains 1500 bacteria initially and doubles every hour.

i.e. a = 1500 and b= 2

Then, the function N that models the number of bacteria after t hours will be :

$N(t)=1500(2)^t$

To find , the number of bacteria after 24 hours , we put t= 24 in above equation , we get

$N(24)=1500(2)^{24}\\\\=1500(16777216)=25165824000$

Hence, the number of bacteria after 24 hours is 25165824000.

7 0

3 years ago