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stepladder [879]
3 years ago
15

The area covered by a marsh, A, starts at 11500 acres and drops by a 1/4 each year for n years. Write a formula for A(n).

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
8 0

The formula for  that represent the area covered by a marsh A(n) is A(n)=11500(\frac{1}{4} )^n.

An exponential decay is given by the function:

y = abˣ

Where a is the initial value of y, b is a constant which is less than 1, y, x are variables.

Since the area covered by a marsh, A, starts at 11500 acres, hence a = 11500. Since the area drops by 1/4 each year for n years, hence:

A(n)=11500(\frac{1}{4} )^n

Therefore the formula for A(n) is A(n)=11500(\frac{1}{4} )^n

Find out more at: brainly.com/question/20898622

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Answer:

f'(x) > 0 on (-\infty ,\frac{1}{e}) and f'(x)<0 on(\frac{1}{e},\infty)

Step-by-step explanation:

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f'(x)>0

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2) Then let's find the critical point of this function:

f'(x)=\frac{\mathrm{d} }{\mathrm{d} x}[6-2^{2x}]=\frac{\mathrm{d} }{\mathrm{d}x}[6]-\frac{\mathrm{d}}{\mathrm{d}x}[2^{2x}]=0-[ln(2)*2^{2x}*\frac{\mathrm{d}}{\mathrm{d}x}[2x]=-ln(2)*2^{2x}*2=-ln2*2^{2x+1\Rightarrow }f'(x)=-ln(2)*2^{2x}*2\\-ln(2)*2^{2x+1}=-2x^{2x}(ln(x)+1)=0

2.2 Solving for x this equation, this will lead us to one critical point since x'  is not defined for Real set, and x''=\frac{1}{e}≈0.37 for e≈2.72

x^{2x}=0 \ni \mathbb{R}\\(ln(x)+1)=0\Rightarrow ln(x)=-1\Rightarrow x=e^{-1}\Rightarrow x\approx 2.72^{-1}x\approx 0.37

3) Finally, check it out the critical point, i.e. f'(x) >0 and below f'(x)<0.

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3 years ago
Elizabeth drove two-fifths of a mile in 30 seconds. Which of the following shows
hichkok12 [17]

Answer:

c.

Step-by-step explanation:

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Answer:

B

Step-by-step explanation:

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From the graph, we can see that (0,1) gives 1 as a y-value. Thus, when x is 0, y is 1.

Therefore, f(0)=1.

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3 years ago
A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G. What are the coordinates
I am Lyosha [343]

Given:

A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.

To find:

The coordinates of point G.

Solution:

Section formula: If a point divide a line segment with end points (x_1,y_1) and (x_2,y_2) in m:n, then the coordinates of that point are

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G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)

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2 years ago
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tigry1 [53]

Answer:

2

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Hope this helps.

-Amelia

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