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There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question

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Solution.

Initial population = 205

After 1 year, population = 205 - 7 = 198

After 2 years , population = 198 - 7 = 191

After 3 years , population = 191 - 7 = 184

We can generate a table of value for the changes

[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]

One point on the line = (0, 205)

[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]

The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park

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