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A roller coaster is currently traveling at a speed of 49 miles per hour (mph). The coaster's speed will increase at a constant rate of 17mph every 2 seconds until the coaster reaches its top speed 5 seconds from now. If t <= 5, which function best represents the roller coaster's speed, in miles per hour, t seconds from now? Choose 1 answer: (A) f(t)=49+8.5 t (B) f(t)=49+17 t (c) f(t)=49 t+9.8 t (D) f(t)=49 t+17 t

A roller coaster is currently traveling at a speed of 4949 miles per hour (mph). The coaster's speed will increase at a constant rate of 17mph 17 \mathrm{mph} every 22 seconds until the coaster reaches its top speed 55 seconds from now. If t≤5 t \leq 5 , which function best represents the roller coaster's speed, in miles per hour, t t seconds from now?\newlineChoose 11 answer:\newline(A) f(t)=49+8.5t f(t)=49+8.5 t \newline(B) f(t)=49+17t f(t)=49+17 t \newline(C) f(t)=49t+9.8t f(t)=49 t+9.8 t \newline(D) f(t)=49t+17t f(t)=49 t+17 t

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Q. A roller coaster is currently traveling at a speed of 4949 miles per hour (mph). The coaster's speed will increase at a constant rate of 17mph 17 \mathrm{mph} every 22 seconds until the coaster reaches its top speed 55 seconds from now. If t≤5 t \leq 5 , which function best represents the roller coaster's speed, in miles per hour, t t seconds from now?\newlineChoose 11 answer:\newline(A) f(t)=49+8.5t f(t)=49+8.5 t \newline(B) f(t)=49+17t f(t)=49+17 t \newline(C) f(t)=49t+9.8t f(t)=49 t+9.8 t \newline(D) f(t)=49t+17t f(t)=49 t+17 t
  1. Problem Understanding: Understand the problem.\newlineWe need to find a function that represents the roller coaster's speed as it increases at a constant rate from its current speed of 49 mph49\,\text{mph}. The speed increases by 17 mph17\,\text{mph} every 2 seconds2\,\text{seconds}, and we are looking at a time frame of up to 5 seconds5\,\text{seconds}.
  2. Rate of Increase: Determine the rate of increase per second.\newlineThe coaster's speed increases by 17 mph17 \text{ mph} every 2 seconds2 \text{ seconds}. To find the rate of increase per second, we divide 17 mph17 \text{ mph} by 2 seconds2 \text{ seconds}.\newlineRate of increase per second = 17 mph2 seconds=8.5 mph per second\frac{17 \text{ mph}}{2 \text{ seconds}} = 8.5 \text{ mph per second}.
  3. Function for Speed: Write the function for the roller coaster's speed.\newlineSince the speed increases at a constant rate, we can represent this as a linear function of time tt, where tt is in seconds. The function starts with the initial speed of 49 mph49\,\text{mph} and adds the increase in speed, which is 8.5 mph8.5\,\text{mph} multiplied by the number of seconds tt.\newlinef(t)=initial speed+(rate of increase per second×time)f(t) = \text{initial speed} + (\text{rate of increase per second} \times \text{time})\newlinef(t)=49+(8.5×t)f(t) = 49 + (8.5 \times t)
  4. Matching the Function: Match the function with the given choices.\newlineThe function we derived is f(t)=49+8.5tf(t) = 49 + 8.5t, which matches choice (A).

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