Part 1 -Sample roller coasters warm up: Fanny and Elena enjoy roller coasters. Whenever a new roller Coaster opens near their town,
they try to be among the first to ride. One Saturday, the two friends decide to ride a new
coaster. While waiting in line, Fanny notices that part of this coaster resembles the graph of a
polynomial function that they have been studying in their math class.
The brochure for the coaster says that, for the first 10 seconds of the ride, the height of the
coaster can be determined by H(t) = 0.3t-t+ 21t where t is the time in seconds and h
is the height in feet.
1. Find the height of the coaster at t = 0 second. Explain why this answer makes sense.
2. Evaluate H(10) to find the height of the roller coaster at t = 10 seconds.
3. Graph H(t) using a calculator or a computer program for t=0 to t = 10 seconds.
4. During the first 10 seconds of the ride, is the rollercoaster going up and/or going down?
Is the slope constant?

Step-by-step explanation:

h(t) = 0.3t -t +21t , t=time and h=height

1.

at t=0  the hight is h=0

h(0) = 0.3*0 -0 +21*0 = 0

It makes sense that at the time 0 seconds when the rollercoaster did not leave the hight is 0 feet.

2.

for t=10 substitute t with 10

h(10) = 0.3*10 -10 +21*10 = 3 -10 +210 = 203

3. see graph

4. the rollercoaster is going up

what graph

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.