The given data about the population of deer in the forest over the five-years period is given by the exponential equation which is the option C) exponential [tex]y = 91(0.77)^{x}[/tex]
Step-by-step explanation:
- The given data of population of deer over 5 years are decreasing in number.
- Therefore, the equations that are represented with addition symbol can be eliminated.
- From this information, the options A), B) and C) can be eliminated.
The only option C) is remaining which could be the right equation to represent the given data.
So, let us check the given data with the exponential equation [tex]y = 91(0.77)^{x}[/tex]
In the above exponential equation,
- x represents the number of years.
- y represents the estimated population.
Now, substitute x= 0 years and check if y= 91,
⇒ [tex]y= 91(0.77)^{0}[/tex]
anything which as a power equals to 1.
Therefore, y=91 in 0 years.
Similarly,
⇒ [tex]y = 91(0.77)^{1}[/tex] = 70.7 ≈ 70
⇒ [tex]y = 91(0.77)^{2}[/tex] = 53.9 ≈ 54
⇒ [tex]y = 91(0.77)^{3}[/tex] = 41.5 ≈ 42
⇒ [tex]y = 91(0.77)^{4}[/tex] = 31.9 ≈ 32
The exponential equation [tex]y = 91(0.77)^{x}[/tex] provides the exact data about the population of deer in the table.
