Respuesta :
The general exponential equation modelling the change per year in a value is given as:
[tex]A= A_{o}(1-x)^{t} [/tex]
Here,
A₀ is the original amount
A is the amount after t years
x is the change per year. For decreasing values, x will be negative
t is the number of years.
In the given case, the original value of Area is 1500. The change per year is 4.8%, in decimal this equals 0.048. Since the area is decreasing the value of x will be - 0.048.
The area Y that the forest covers after t years can be written as:
[tex]Y=1500(1-0.048)^{t} \\ \\ Y=1500(0.952)^{t} [/tex]
The above equation shows the relation between the forest area and the number of years since the environmental study.
[tex]A= A_{o}(1-x)^{t} [/tex]
Here,
A₀ is the original amount
A is the amount after t years
x is the change per year. For decreasing values, x will be negative
t is the number of years.
In the given case, the original value of Area is 1500. The change per year is 4.8%, in decimal this equals 0.048. Since the area is decreasing the value of x will be - 0.048.
The area Y that the forest covers after t years can be written as:
[tex]Y=1500(1-0.048)^{t} \\ \\ Y=1500(0.952)^{t} [/tex]
The above equation shows the relation between the forest area and the number of years since the environmental study.
Answer:
[tex]y=1500(0.952)^{t}[/tex]
Step-by-step explanation:
Explicit formula of an exponential function is given by
[tex]A_{t}=A_{0}(b)^{t}[/tex]
[tex]A_{t}[/tex] = Area covered by the forest after time t
[tex]A_{0}[/tex] = Initial area covered by the forest
b = (1 - r)
and r = rate of decay of the forest area
t = time in years
[tex]A_{t}=1500(1-0.048)^{t}[/tex]
[tex]y=1500(0.952)^{t}[/tex]
Therefore, function representing relationship between y and t will be
[tex]y=1500(0.952)^{t}[/tex]
