3.5--Equation Solving and Modeling
Solve algebraically. Round to 3 places if necessary:
1/4
1)
54 (1/3)
3)
13 + 7e
= 6
0.021x
= 99
2x
2)
1.13 = 47
4)
23 - 4 ln (x + 7) = 9
1
3.5--Equation Solving and Modeling
Solve algebraically. Round to 3 places if necessary:
5)
-2 + (e x - e-x )/3 = 1
6)
State the domain of the following function, then graph it:
f(x) = 5 log x - log (x-2)
y
10
5
­10
­5
5
10
x
­5
­10
2
3.5--Equation Solving and Modeling
Orders of magnitude are used to compare quantities that
are very far apart. For example...
Starting with the smaller (lighter, shorter, etc.) number, an
order of magnitude is gained every time you multiply by ten.
Logarithmic scales are commonly used in science. As a result,
an order of magnitude represents...
~1 unit on the Richter Scale used for measuring earthquakes.
~1 unit on the pH scale in chemistry.
~10 decibels of sound intensity.
7)
How many times more severe is an earthquake measuring
7.7 on the Richter Scale than one measuring 4.7?
8)
How many times more acidic is a glass of Pepsi with a pH
of 4.0 than a glass of milk with a pH of 6.5?
9)
How many times louder is a rock concert measuring 115
decibels than a normal conversation at 65 decibels?
3
3.5--Equation Solving and Modeling
Newton's Law of Cooling
T = Ts + ( To - Ts ) e-kt
10)
T
= current temperature of object
To
= original temperature of object
Ts
= temperature of surroundings
A pot of chili has been cooking at 250o F. The chili is
removed from the stove and placed into a refrigerator
with an internal temperature of 40o F. After ten minutes
in the fridge, the chili's temperature is 167o F. Find the
new temperature of this chili after another 15 minutes:
4