Respuesta :
Answer:
The area of forest after 8 years , decreases at the rate of 7.25% is 2081.108 square kilometers .
Step-by-step explanation:
Given as :
The initial area of forest = 3800 square kilometer
The rate of decrease of area every year = r = 7.25 %
The time period for its decrease = t = 8 years
Let The forest area after 8 years = A square kilometers
Now, According to question
The forest area after 8 years = Initial area of forest × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
or, The forest area after 8 years = 3800 km² × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
or, The forest area after 8 years = 3800 km² × [tex](1-\dfrac{\textrm 7.25}{100})^{\textrm 8}[/tex]
Or, The forest area after 8 years = 3800 km² × [tex](0.9275)^{8}[/tex]
Or, The forest area after 8 years = 3800 km² × 0.54766
Or, The forest area after 8 years = 2081.108 km²
So, Area of forest after 8 years = 2081.108 km²
Hence The area of forest after 8 years , decreases at the rate of 7.25% is 2081.108 square kilometers . Answer
Answer:
Area of forest after 8 years [tex]\boldsymbol\approx[/tex] 2081.11 [tex]\mathbf{km^{2}}[/tex]
Step-by-step explanation:
Rate of decrements is 7.25% per year.
Let us create a function 'f(x)' which gives the area of forest left after 'x' years.
f(0) means the initial year when the area is 3800 [tex]\textrm{km}^{2}[/tex].
f(0) = 3800
f(1) means the area left after one year passed when the area decreased by 7.25% than previous year which is 3800 [tex]\textrm{km}^{2}[/tex]
f(1) = 3800 - 7.25% of 3800 = [tex]3800-\frac{7.25}{100}\times3800[/tex] = [tex]3800(1-\frac{7.25}{100})[/tex] = [tex]3800(\frac{92.75}{100})[/tex]
f(2) means the area left after two year passed when the area decreased by 7.25% than previous year which is f(1)
f(2) = f(1) - 7.25% of f(1) = [tex]\textrm{f}(1)(\frac{92.75}{100})[/tex] = [tex]3800(\frac{92.75}{100})(\frac{92.75}{100})[/tex] = [tex]3800(\frac{92.75}{100})^{2}[/tex]
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Similarly [tex]\mathbf{f(x)=3800(\frac{92.75}{100})^{x}}[/tex]
[tex]\textrm{f}(8)=3800(\frac{92.75}{100})^{8}\approx2081.11 \ \textrm{km}^{2}[/tex]
[tex]\mathbf{\therefore f(8)\approx2081.11 \ km^{2}}[/tex]
