Download Pre – Calculus · 7 - Telluride School District R-1

Pre – Calculus  7.3  Examples
Name: _________________
1) Lizard Mass Problem: Curators at Scorpion Gulch Zoo measured the mass of lizards of
varying lengths, finding these data:
a) What pattern do the data follow? What kind
of function has this pattern?
b) By following the pattern, predict the mass of
a 24-cm lizard and of a 30-cm lizard?
Length
(cm)
Mass
(g)
3
2.7
6
21.6
9
72.9
12
172.8
15
337.5
c) Find the particular equation for a function
that fits this data.
d) The largest kind of lizard is the Komodo dragon. Use your equation to predict the
mass of a Komodo dragon that is 110 cm long.
e) Based on this mathematical model, how long would you expect a 1–kg lizard to
be?
2) Computer Iterations Problem: When a computer runs a program, it takes a certain fixed
amount of time to compile the program and then a variable amount of time to run the
program. The running time depends on how many iterations are performed (that is, how
many times the program repeats itself). This table shows the number of seconds it takes a
particular computer to run programs with a given number of iterations.
a) What pattern do the data follow? What kind
of function has this pattern?
b) By following the pattern, predict how long it
would take for 1000 iterations.
c) Find the particular equation for a function
that fits this data.
Iterations
Seconds
200
8.7
300
12.2
400
15.7
500
19.2
600
22.7
d) At what rate (in seconds per iteration) does the computer perform the iterations?
What part of the equation gives you this number?
e) How long does the computer take to compile the program before it starts
performing iterations? What part of the equation gives you this number?
f) If the program takes 47.3 sec to run, how many iterations did the computer
perform?
3) Savings account problem: On Joe’s 10th birthday, his parents started a savings account
for him. This table shows the amount of money in the account on several subsequent
birthdays.
a) What pattern do the data follow? What
kind of function has this pattern?
b) Follow the pattern forward to find out how
much will be in the account on Joe’s 16th
and 17th birthday.
Age
(Years)
Amount
(Dollars)
12
$3630.00
13
3993.00
14
4392.30
15
4831.53
c) Follow the pattern backwards to find out how much money was invested on Joe’s
10th birthday.
d) By what percentage does his money increase each year?
e) Find the particular equation for a function that fits this data.
f) If Joe leaves his money in the account and the interest rate remains the same, how
much money will be in the account on his 65th birthday?