The function that grows the fastest is A. 𝑎(𝑡)=𝑡^5/2.

Here's why:

1. Compare the highest degree of the polynomial functions. The highest degree is the power of the variable that has the highest value. In this case, function A has the highest degree (5/2 or 2.5), which is higher than the degrees in functions B (2) and E (2).

2. For function C, the natural logarithm function ln(t/100), the growth rate is slower than any polynomial function for large t.

3. For function D, e(t)=e, this is a constant function and does not grow at all as t increases.

Therefore, function A grows the fastest.

Question

The function that grows the fastest is A. 𝑎(𝑡)=𝑡^5/2.

Here's why:

1. Compare the highest degree of the polynomial functions. The highest degree is the power of the variable that has the highest value. In this case, function A has the highest degree (5/2 or 2.5), which is higher than the degrees in functions B (2) and E (2).

2. For function C, the natural logarithm function ln(t/100), the growth rate is slower than any polynomial function for large t.

3. For function D, e(t)=e, this is a constant function and does not grow at all as t increases.

Therefore, function A grows the fastest.

Knowee AI · Accepted Answer

The function that grows the fastest is A. 𝑎(𝑡)=𝑡^5/2.

Here's why:

1. Compare the highest degree of the polynomial functions. The highest degree is the power of the variable that has the highest value. In this case, function A has the highest degree (5/2 or 2.5), which is higher than the degrees in functions B (2) and E (2).

2. For function C, the natural logarithm function ln(t/100), the growth rate is slower than any polynomial function for large t.

3. For function D, e(t)=e, this is a constant function and does not grow at all as t increases.

Therefore, function A grows the fastest.

Which of the following functions grows the fastest?A.𝑎(𝑡)=𝑡52a(t)=t 25 B.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t C.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )D.𝑒(𝑡)=𝑒e(t)=eE.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −t

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Which of the following functions grows the fastest?A.𝑎(𝑡)=𝑡52a(t)=t 25​ B.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t​ C.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )D.𝑒(𝑡)=𝑒e(t)=eE.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −t

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Which of the following functions grows the fastest?A.𝑎(𝑡)=𝑡52a(t)=t 25 B.𝑐(𝑡)=𝑡2−5𝑡c(t)= t 2 −5t C.𝑖(𝑡)=ln⁡(𝑡100)i(t)=ln(t 100 )D.𝑒(𝑡)=𝑒e(t)=eE.𝑔(𝑡)=3𝑡2−𝑡g(t)=3t 2 −t