A scientist observed the population of butterflies in two different fields. In field A, the population of butterflies is defined by the function A(x) = 50(1.2)3x, where x represents the number of years.

In field B, the population of butterflies is defined by the function B(x) = 25(1.728)x, where x represents the number of years.

Which statement is true?
A.
The initial butterfly population of field B is smaller than the initial butterfly population of field A, but the population of both fields is decreasing at the same rate.

B.
The initial butterfly population of field B is greater than the initial butterfly population of field A, but the population of both fields is decreasing at the same rate.

C.
The initial butterfly population of field B is smaller than the initial butterfly population of field A, but the population of both fields is increasing at the same rate.

D.
The initial butterfly population of field B is greater than the initial butterfly population of field A, but the population of both fields is increasing at the same rate.

the answer is a

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

my name jeff

step-by-step explanation:

natural disasters at one point james charles' career