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3 years ago

7

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate

parameter of 7.4% per hour. How many hours does it take for the size of the sample to double

1 answer:

Tom [10]3 years ago

8 0

Answer:18.12

Step-by-step explanation:

You might be interested in

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given.</em>

<em /> $\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution/u-solve</em>.

Set <em>u</em>:
$\displaystyle u = 4 - x^2$
[<em>u</em>] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[<em>du</em>] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

<u>Step 3: Integrate Pt. 2</u>

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[<em>u</em>] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to <em>find</em> the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0

2 years ago

PLEASE HELP <br> 3/4% of 120 equals

sammy [17]

Answer:

90

Step-by-step explanation:

so first do 120 divided by 4 is 30. Then multiply it by 3 to get 90.

7 0

2 years ago

Read 2 more answers

Two times p plus five is greater than or equal to three times p minus ten

hjlf

Answer:

2p + 5 ≥ 3p - 10

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which is the solution set of the inequality 15y-9<36

m_a_m_a [10]

15y - 9 <36.
Add 9 to each side.

15y- 9 (+9) < 36 + 9.
15y < 45.
y < 3.
Hope it helps! :)

7 0

3 years ago

Read 2 more answers

PROBLEM. 11.1: Rewrite These! Rewrite each quotient as a sum or a difference.

Jet001 [13]

Answer:

1. (4x-10)/2

4x/2 - 10/2

2x - 5

2. (1-50x)/-2

1/-2 -50x/-2

25x - 1/2

3. 5(x + 10)/25

(5x + 50)/25

5x/25 + 50/25

1/5 x + 2

4.(-0.2x + 5)/2

-0.2x/2 + 5/2

-0.1x + 2.5

3 0

3 years ago