MATH 190 Midterm: MATH 190 Louisville Exam 2 160303
MATH 190–03 Exam #2 Name:
This test is closed-book and closed-notes. No calculator is allowed for this test. For full credit
show all of your work (legibly!), unless otherwise specified. Answers should be simplified down to
arithmetic expressions whenever possible, but unsimplifiable exponentials and common or natural
logarithms may be left unevaluated.
1. (15 points) Answer the following questions about growth and decay.
(a) (5 points) A metal ingot is removed from a furnace into a warm metalworking studio; its
temperature tminutes after removal is given by the function f(t) = 90 + 410e−0.05t. How
long will it take the ingot to cool to 200◦F?
(b) (4 points) You have $500 invested in an account which bears 2% annual interest, com-
pounding quarterly. Produce a function describing the value in your account after tyears.
(c) (6 points) You hope to cash the account from the previous question out when it reaches
a balance of $600. Based on the function from the previous question, how many years do
you need to wait until you can do so?
2. (20 points) Solve the inequality s+3
(s−1)2≤1
s+2 .
1/15
2/20
3/20
4/15
5/15
6/15
Σ/100
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Document Summary
For full credit show all of your work (legibly! How long will it take the ingot to cool to 200 f? (b) (4 points) you have invested in an account which bears 2% annual interest, com- pounding quarterly. Produce a function describing the value in your account after t years. (c) (6 points) you hope to cash the account from the previous question out when it reaches a balance of . Based on the function from the previous question, how many years do you need to wait until you can do so: (20 points) solve the inequality s+3 (s 1)2 1 s+2. If so, identify which it is and what its value is. (c) (5 points) determine the x-intercepts of this quadratic if they exist (explicitly stating if they do not exist), and its y-intercept. Label which is which: (15 points) answer the following questions concerning logarithms. (a) (5 points) solve for x in the exponential equation 5 2(x2.
