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1 year ago

What is the exponential function that best models the number of gnats the scientists have

Mathematics

1 answer:

IrinaVladis [17]1 year ago

6 0

Answer:

(b) f(x) = 12.5(1.6^x)

Step-by-step explanation:

An exponential model is generally of the form ...

f(x) = a·b^x

where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.

<h3>Growth factor</h3>

The ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)

An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.

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Solve for X

tigry1 [53]

Answer:

$x = \pm e^{-1}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Solving quadratics
Multiple roots

Algebra II

Logarithms
Euler's number e

Step-by-step explanation:

Step 1: Define

$\displaystyle ln(x^2) = -2$

Step 2: Solve for x

Raise both sides by e: $e^{\displaystyle ln(x^2)} = e^{-2}$
Simplify equation: $x^2 = e^{-2}$
Square root both sides: $x = \pm e^{-1}$

7 0

2 years ago

Read 2 more answers

The sector of a circle is shown below. It has a radius of 10 centimeters and a central

disa [49]

Answer:

1) 8.9 cm

2) 44.5 cm^2

Step-by-step explanation:

a) we want to calculate the length of the arc

Mathematically, we use the formula for the length of an arc

That will be ;

theta/360 * 2 * pi * r

theta = central angle = 51

r is radius = 10 cm

so we have ;

51/360 * 2 * 22/7 * 10 = 8.9 cm

2) The area of the sector is;

theta/360 * pi * r^2

51/360 * 22/7 * 10^2

= 44.5 cm^2

5 0

3 years ago

PLEASE HELP DUE NOW!!! WILL MARK BRAINLIEST!!!

Ulleksa [173]

Answer: -10, 10

Step-by-step explanation:

first lets add the two equations. add the x's, add the y's, add the constants on the right.

we get

0x - 1y = -10

so then divide --10 by -1 because we do the opposite operations to both sides

and we get y = 10

now substitute y = 10 into the first equation

-10x - 9(10) = 10

and then we get -10x - 90 = 10

now add 90 to both sides

-10x = 100

divide 100 by -10

x = -10

y = 10

checks out

EPIC. STAY EPIC AND AWESOME FRIEND.

3 0

2 years ago

The vertex angle of isosceles triangle is 110 degrees. what are the measures of the base angles

dalvyx [7]

Answer:

35°

Step-by-step explanation:

The base angles of an isosceles triangle are congruent , then

base angles = $\frac{180-110}{2}$ = $\frac{70}{2}$ = 35°

3 0

2 years ago

If a=4b^2 and b=-1/2e^2, what is the value of a to the nearest tenth?

Maru [420]

To answer, it is assumed that e here is the Euler number which is equal to 2.718. Substitute this value to the e of the second equation to get the value of b.
b = 0.5(2.718^2) = 3.6945
Then, we substitute this value to the first equation to get the value of a.
a = 4(3.6945^2) = 54.498
Thus, the answer is approximately equal to 54.5.

3 0

3 years ago