The function below describes the population of caribou in a tundra, where f(t) represents the number of caribou, in hundreds, and t represents the time, in years.

f(t)=1.8(1.2)^t

initially, the tundra has caribou, and every , the number of caribou increases by a factor of .

  Initially, the tundra has 180 caribou, and every year , the number of caribou increases by a factor of 1.2 .

Step-by-step explanation:

"Initially" generally means "when t=0." Put 0 where t is in the function and evaluate it:

  f(0) = 1.8(1.2)^0 = 1.8(1) = 1.8 . . . . . hundreds

1.8 hundreds is 1.8×100 = 180.

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t is in years, so the simplest choice for the second blank in the statement is "year".

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The exponent of 1.2 is t, which means that 1.2 is a factor of the expression the number of times specified by t.

  for t=0, f(0) = 1.8

  for t=1, f(1) = 1.8(1.2)

  for t=2, f(2) = 1.8(1.2)(1.2)

  for t=3, f(3) = 1.8(1.2)(1.2)(1.2)

Perhaps you can see that every year, the number increases by a factor of 1.2.

You could put "3 years" in the second blank, then the third blank would be 1.2³ = 1.728. While correct, it is probably not what is expected by your answer checker.

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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