Answer:
about 81 years
Step-by-step explanation:
A graphing calculator can give you the answer easily.
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You can solve the problem algebraically by putting in the given number and solving for t.
30000 = 32000/(1 +12.8e^(-.065t))
12.8e^(-.065t) = (32000/30000) -1 = 1/15
e^(-.065t) = 1/(15·12.8) = 1/192 . . . . . divide by 12.8
-0.065t = ln(1/192) ≈ -5.257 . . . . . . take the natural log
t = -5.257/-0.065 ≈ 80.88 . . . . . . . .divide by the coefficient of t
It will take about 81 years for the number of trees to reach 30,000.
ANSWER
D. 224
EXPLANATION
The given series is
The first term of this series is
The last term of this series is:
The sum of the first n-terms of the series is calculated using the formula,
When you make a drawing with the instructions, and call x the altitude of the plane and y the distance from the angle 72 ° to the point straight below the plane, you obtain these equations
tan(55°) = x / (2.2 + y)
tan (72°) = x / y
You solve y from the second equation
y = x / tan(72°)
Substitute y in the first equation
tan (55°) = x /(2.2 + x/tan(72°)
Solve for x:
x = tan(55)[2.2 + x/tan(72) ]
x = tan(55) (2.2) + x tan(55)/tan(72)
x - x tan (55)/tan(72) = 2.2 tan (55)
Now substitute the values of the tangents
tan (55) = 1.4281
tan(72) = 3.0777
x - 0.464x = 3.1419
x = 3.1419 / (1-0.464) =5.86 m
Ah ... it is a toy plane! I guess.