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).
1 answer:
The formula for that represent the area covered by a marsh A(n) is .
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:
Therefore the formula for A(n) is
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Answer:
Step-by-step explanation:
First, you gotta work out the hypotenuse of ABC, which is AC.
To do that, you need to figure out the scale factor between the two right-angled triangles. You can do that for this question because this is a similar shapes question.
12.5/5 = 2.5
The scale factor length between the two triangles is 2.5.
You can use 2.5 now to work out AC, so AC would be 13 x 2.5, which gives 32.5.
Now that you've got the hypotenuse and BC of ABC, you can use Pythagoras's theorem to work out the length of AB
Pythagoras's theorem =
a = BC = 12.5
b = AB = we need to work this out
c = AC (the hypotenuse we just worked out) = 32.5
Let's both simplify and rearrange this at the same time so that we have our b on one side.
= 1056.25 - 156.25
b =
b =
b = AB = 30 We've found b or AB, now we can work out the perimeter of ABC.
Perimeter of ABC = AB + BC + AC
= 30 + 12.5 + 32.5
= 75 Here's the perimeter for ABC.