HW 05
Name
Math 1180
Chapter 4
1. Solve these equations for x; give exact answers:
a. 32x+5 = 27x
b. 23x= 71−x
c. log3(7x+ 2) = 1
2. Find the inverse of the following functions; specify the domain and range for each:
a. f(x)=3x+ 1
b. g(x) = x3−2
1
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Math 1180 Homework 5: Solutions for Chapter 4 - Prof. Julienne D. Houck, Assignments of Pre-Calculus
The solutions for homework problems in chapter 4 of math 1180. It includes solving equations for x, finding inverse functions, using the change of base formula, expanding logarithms, and modeling bacterial growth using exponential functions.
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HW 05
Name Math 1180
Chapter 4
- Solve these equations for x; give exact answers:
a. 32 x+5^ = 27x
b. 23 x^ = 7^1 −x
c. log 3 (7x + 2) = 1
- Find the inverse of the following functions; specify the domain and range for each:
a. f (x) = 3x + 1
b. g(x) = x^3 − 2
c. h(x) = ex
d. m(x) = 2 − log(3x + 1)
- Use the change of base formula to calculate the following with your calculator (write out what you do on your calculator—that still counts as work.) If you’d prefer, you may figure them out algebraically instead:
a. log 5 (625)
b. log 2 (64)
c. log 64 (2)
- Expand completely: ln
4 ab^3 3 c^2 d^4
- Use the information in the given table to come up with an exponential model for p(x). (Note that there are many different possibilities for correct answers, so it will be impossible for me to decipher your answer if you do not show your work.)
x 12 57 102 151 193
p(x) 9 17 31 61 109
- Suppose the population of fish in a particular lake is modeled by the equation
P (t) =
1 + 13e−^0.^085 t^
where P (t) is the number of fish living in the lake, and t is the number of months since the beginning of 1990 (that is, t = 0 corresponds to the beginning of January, 1990).
a. How many fish were in the lake at the beginning of 1990?
b. According to the model, what is the maximum number of fish that could be in the lake at any time? (You may look at the graph to figure this out.)
c. Fill in the given table and then plot those points on the given axes. Sketch the graph using these points.
t P (t)
l 0
l 15
l 40
l 50
l 60
l 80
l 100
l 150
- (^) t
P (t)
10 30 50 70 100 150
2000
6000
10,
14,