Rated PG (for Language)

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For each of the first three problems, write an equivalent statement using $f$ and $f'$ notation.

If $f$ is the population of Hicktown,

(a): The population of Hicktown was $5.4$ million in $2018$ .
(b): The population of Hicktown was increasing at a rate of $110000$ people per year in $2018$ .

Joan decides to take a run outside. Let $p(t)$ be the position Joan is from home (east or west) after $t$ minutes. Assume Joan is always traveling in the same eastward direction.

(a): She runs along a flat country road at $100$ meters per minute for $10$ minutes.
(b): She comes to a hill. Over the next $3$ minutes, her velocity drops at a constant rate of $15$ meters per minute each minute.

Joan decides to take a run outside. Let $v(t)$ be Joan’s velocity at time $t$ in meters per minute. Assume Joan is always traveling in the same eastward direction.

(a): She runs along a flat country road at $100$ meters per minute for $10$ minutes.
(b): She comes to a hill. Over the next $3$ minutes, her velocity drops at a constant rate of $15$ meters per minute each minute.

Let $H$ stand for the height of a balloon (in feet above the ground) as a function of time (in minutes). Translate the following into English:

(a): $H(0) = 1000$
(b): $H'(0) = 0$
(c): $H'(5) = -52$
(d): $H(5) - H(0) - -201$

Let $f$ be a function such that $f(0) = 5$ and $3 \leq f'(t) \leq 12$ for all $t$ . What can be said about the value of $f(4)$ ? About $f(-4)$ ?

2024-10-10 13:52:00