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dolphi86 [110]
3 years ago
9

Describe the y-intercept and end behavior of the following graph:

Mathematics
1 answer:
andre [41]3 years ago
4 0

Answer:

Based on graph description ...

  • end behavior: (-∞, +∞), (+∞, -∞)
  • y-intercept: (0, -4)

Based on what appear to be answer choices ...

  • end behavior: (-∞, ∞), (+∞, -6)
  • y-intercept: (0, -5)

Step-by-step explanation:

<u>End behavior</u>

"Starts at top left" means the function approaches +∞ as x approaches -∞.

"Continues decreasing to the bottom right" seems to mean the function approaches -∞ as x approaches +∞.

(While an exponential decay function "continues decreasing", it approaches a limit. Your description of the graph says nothing about that, so we assume it is an odd-degree polynomial function with a negative leading coefficient.)

__

<u>Y-intercept</u>

"Crosses the y axis at negative 4" means the y-intercept is (0, -4).

_____

<em>Comment on problem statement discrepancies</em>

Perhaps you intended to describe the graph as "approaching -6 at the bottom right." That would match a description, "The graph approaches y = −6 to the right." However, your offered choice of (0, -5) for the y-intercept does not match the verbal description of "crosses the y axis at negative 4."

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Help me with these questions
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Answer: a = 4, b = 163,422

<u>Step-by-step explanation:</u>

P = P_{0} e^{kt}   P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.

Part a) What do we know?

P = 7003

P₀ = unknown

k = .21 <em>(converted 21% into a decimal)</em>

t = 36 yrs <em>(2006 - 1970) </em>

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7003 = P_{0} e^{7.56}

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\frac{7003}{1920} = P_{0}

3.6 = P₀

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Part b) What do we know?

P = unknown

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k = .21 <em>(converted 21% into a decimal)</em>

t = 15 yrs <em>(2021 - 2006) </em>

P = P_{0} e^{kt}   <em>need to solve for P₀</em>

P = 7003 e^{(.21)(15)}

P = 7003 e^{3.15}

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*************************************************************

Answer: 2, -1

<u>Step-by-step explanation:</u>

eˣ² = eˣ * e²

eˣ² = eˣ⁺²

x² = x + 2

x² - x - 2 = 0

(x - 2)(x + 1) = 0

x - 2 = 0      or      x + 1 = 0

 x = 2          or         x = -1

Check both answer for validity:

eˣ² = eˣ⁺²

e⁴ = e⁴     or   e¹ = e¹

TRUE             TRUE

*****************************************

Answer: 0 = ln 1

<u>Step-by-step explanation:</u>

e^{-10} = \frac{1}{e^{10}}

ln(e^{-10}) = ln(\frac{1}{e^{10}})

-10 = ln 1 - 10   <em>log rules say division is subtraction</em>

 0 = ln 1



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