ExponentialsModels Logarithms Compositions and Inverses Systems End RoundThemeFinal Jeopardy

Exponentials 100 Points   2 5 = x

Exponentials 100 Points X = 32

Exponentials 200 Points   X 0 = ?

Exponentials 200 Points X 0 = 1

Exponentials 300 Points   Who is “e” named after and what type of number is it?

Exponentials 300 Points Euler, irrational

Exponentials 400 Points   Sketch f(x) = e x, and identify its intercepts, asymptotes (if any), and domain and range.

Exponentials 400 Points Intercepts: X-int: none Y-int: (0,1) Asymptotes: y = 0 D: all real #’s R: y>0

Exponentials 500 Points Sketch a graph of the following function: f(x) = -2 x +3  

Exponentials 500 Points

Logarithms 100 Points Write the following logarithm in exponential form: log 3 81 = 4  

3 4 = 81 Logarithms 100 Points

Logarithms 200 Points Write the following exponential equation in logarithmic form: 8 2 = 64  

Logarithms 200 Points log 8 64 = 2

Logarithms 300 Points   Expand the following expression: log4x 2 y

log4 + 2logx + logy Logarithms 300 Points

Logarithms 400 Points Solve: 2 ln e 6 – ln e 5  

Logarithms 400 Points 7

Logarithms 500 Points Condense the following expression: 4[ ln z + ln(z + 5)] – 2 ln(z – 5)  

Logarithms 500 Points ln z 4 (z + 5) 4 (z – 5) 2

o Compositions&Inverse 100 Points f(x) = 2x 2 – 1g(x) = 3x – 3 Find (g f)(x).  

Compositions&Inverse100 Points 6x 2 – 6

Compositions&Inverse 200 Points   f(x) = 2x 2 – 1g(x) = 3x – 3 Find (f + g)(x).

2x 2 + 3x – 4 Compositions&Inverse 200 Points

Compositions&Inverse 300 Points Find the inverse of f(x) = 2x – 2  

Compositions&Inverse 300 Points f —1 (x) = 0.5x + 1

Compositions&Inverse 400 Points   What is the inverse of f(x) = x 2 – 3?

Compositions&Inverse 400 Points No Inverse

Compositions&Inverse 500 Points   What is the inverse of f(x) = e x – 4?

Compositions&Inverse 500 Points f -1 (x) = ln(x+1)

Models100 Points A total of $12,000 is invested at an annual interest rate of 9%. Find the balance after 5 years if it is compounded monthly.  

Models100 Points Approximately $18,788.17

Models200 Points   On the day of a child’s birth, a deposit of $25,000 is made in a trust fund that pays 8.75% interest, compounded continuously. Determine the balance in this account on the child’s 25 th birthday.

Models200 Points Approximately $222,822.57

Models300 Points   A deposit of $5000 is made in a trust fund that pays 7.5% interest, compounded continuously. It is specified that the balance will be given to the college from which the donor graduated after the money has earned interest for 50 years. How much will the college receive?

Models300 Points Approximately $212,605.41

Models400 Points The number V of computers infected by a computer virus increases according to the model V(t) = 100e t, where t is the time in hours. Find the number of computers infected after 2 hours.  

Models400 Points 1,000,059.6

Models500 Points An isotope has a half-life of 2,500 years. Its mass after 200 years is 12 grams. What was the initial mass?  

Models500 Points Approximately grams

Systems 100 Points  

(2, -4)

Systems 200 Points  

(-3, -9)

Systems 300 Points  

Infinite number of solutions

Systems 400 Points  

(-1, 3)

Systems 500 Points  

(6, -4, 1)

Elimination

FINAL JEOPARDY What is the name of the three variable elimination we learned in class yesterday, and who is it named after?  

FINAL JEOPARDY Gaussian Elimination, named after Gauss