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Darya [45]
3 years ago
7

According to the growth model, how many trees will there be after 50 years? Details below

Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0

Answer: Third Option

f(t)=21,386

Step-by-step explanation:

We know that the equation that models the number of trees in the forest is:

f(t)=\frac{32,000}{1+12.8e^{-0.065t}}

Where t represents the time elapsed in years

To calculate the number of trees after 50 years substitute t = 50 in the equation

f(t)=\frac{32,000}{1+12.8e^{-0.065(50)}}

f(t)=21,386

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\bold{ELIMINATION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8\\y=x+4&\TEXT{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y=-x+8\\-y=-x-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=-2x+4\qquad\text{add}\ 2x\ \text{to both sides}\\.\qquad2x=4\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}

\bold{SUBSTITUTION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8&(1)\\y=x+4&(2)\end{array}\right\\\\\text{Substitute (1) to (2)}\\\\-x+8=x+4\qquad\text{subtract 8 from both sides}\\-x=x-4\qquad\text{subtract}\ x\ \text{from both sides}\\-x-x=-4\\-2x=-4\qquad\text{divide both sides by (-2)}\\\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}

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