Unit 5 Exponential & Logarithmic Functions
S1-MHF4U
Name:______________________________
U5A-(Lesson 1-6) Due date: December 13, 2022 @ 6:30 pm
Ultimate Due Date: December 15, 2022 @ 6:30 pm
UNIT 5 – ASSIGNMENT
Exponential & Logarithmic Functions
TOTAL MARK: 38
Instructions: Show all work for full marks. Add space if you need to.
Submit ONE FILE (PDF) under Unit 5 Assignment Folder in BrightSpace.
A) Knowledge/Understanding
1. Complete each of the sentences. No need to show work. [ 5 ]
a) The inverse of is ___________________? = ??? ?
) Rewrite in exponential form: ___________________log
5
? = 3?
c) Rewrite in logarithmic form: ___________________?12 = 3? + 1
d) Write as a single logarithm: ___________________
log 13
log 5
e) Write as a single logarithm: (Show your work) _____________????4 + 12 ????
4
1
2. Solve the following equations. Leave answers in exact form. [ 3, 3 ]
a) 1252? = 5
?−3
625
) 1 − log (2? + 3) = log ? + 1( )
B) Application
4. One yeast colony of 200 cells is growing exponentially by 10% each hour. Anothe
yeast colony of 1000 cells is diseased and its population is decreasing by 20% each
hour. At what time (if any) will the two colonies have the same population?
Only alge
aic solutions will be accepted. [ 4 ]
2
5. The height of a drone in metres over time in minutes is given by
. The height of a second drone in metres over time in minutes is?(?) = 3 − log
2
(? − 1)
given by . Determine the time when the two drones will be at?(?) = log
2
? + log
2
(? + 2)
the same height and state the height as well. Only alge
aic solutions will be accepted. [ 5 ]
C) Thinking/Inquiry
[ 4 ]
6. Given that is the base function of the transformed function? ?( ) = 3? ? ?( ) = 81(3)?−2 − 5
a) Create an equation to describe without the use of a vertical stretch.?(?)
) Create an equation to describe without the use of a horizontal translation .?(?)
3
7. If logbn
2 = 5, determine the value of logn
3. Use laws of logarithms. [ 4 ]
D) Communication
8. Given XXXXXXXXXX2x) + 3?(?) = − 2 log
a) Determine the following information; show your calculations. [ 6 ]
2 (6 - 2x) + 3 ?(?) = − 2 log
Domain
Range
x-intercept
y-intercept
asymptote
4
) Graph the function. Label all important features for full marks. [ 2 ]
9. Clearly explain, using co
ect mathematical terminology, the difference(s) between the
graph of and [ 2 ]? = ???
6
? ? = ???
6
(36?2)
5