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The number of coyotes, N, reported near a new housing development after t years is given in the table. Which function best models these data? N(t)=0.5t^(3)-t^(2)+5t+1 Number of Coyotes Reported {:[N(t)=2t+1],[N(t)=0.5t^(2)+1],[N(t)=1.95^(t)]:}

The number of coyotes, N N , reported near a new housing development after t t years is given in the table. Which function best models these data?\newlineN(t)=0.5t3−t2+5t+1 N(t)=0.5 t^{3}-t^{2}+5 t+1 \newlineNumber of Coyotes Reported\newlineN(t)=2t+1N(t)=0.5t2+1N(t)=1.95t \begin{array}{c} N(t)=2 t+1 \\ N(t)=0.5 t^{2}+1 \\ N(t)=1.95^{t} \end{array}

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Q. The number of coyotes, N N , reported near a new housing development after t t years is given in the table. Which function best models these data?\newlineN(t)=0.5t3−t2+5t+1 N(t)=0.5 t^{3}-t^{2}+5 t+1 \newlineNumber of Coyotes Reported\newlineN(t)=2t+1N(t)=0.5t2+1N(t)=1.95t \begin{array}{c} N(t)=2 t+1 \\ N(t)=0.5 t^{2}+1 \\ N(t)=1.95^{t} \end{array}
  1. Look at table and functions: Look at the given table and the functions.
  2. Compare function degrees: Compare the degree of each function to the given data.\newlineN(t)=0.5t3−t2+5t+1N(t)=0.5t^{3}-t^{2}+5t+1 is a cubic function.\newlineN(t)=2t+1N(t)=2t+1 is a linear function.\newlineN(t)=0.5t2+1N(t)=0.5t^{2}+1 is a quadratic function.\newlineN(t)=1.95tN(t)=1.95^{t} is an exponential function.
  3. Eliminate linear and exponential: The given data is a cubic function, so we eliminate the linear and exponential functions.\newlineEliminate N(t)=2t+1N(t)=2t+1 and N(t)=1.95(t)N(t)=1.95^{(t)}.
  4. Choose cubic function: Now we have to choose between the cubic function f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d and the quadratic function g(x)=ax2+bx+cg(x) = ax^2 + bx + c.
  5. Choose cubic function: Now we have to choose between the cubic function and the quadratic function. Since the given data is a cubic function, we choose the cubic function. Choose N(t)=0.5t3−t2+5t+1N(t)=0.5t^{3}-t^{2}+5t+1.

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