Logarithms & Exponential Functions
A swimming pool has been exposed to a very high pH level which causes swimmers to have skin irritation and the pool is . What is the pH of the pool if it has a hydrogen ion concentration of 7.23 X 10-6mol/L
pH = -log[H+]
pH = - log 7.23 x 10-6 mol/L
pH = - log 0.00000723
pH = 5.14
A gymnast dismounts the uneven parallel bars. Her height, h, depends on the time, t, that she is in the air modelled by the function, h = -16t2 + 8t + 8. How long will it take the gymnast to reach the ground?
h=-16t2+8t+8
= -16t2-16t+8t+8
= -16t (t-1)-8(t-1)
= (-16t-8) (t-1)
-16t-8=0 t-1=0
-16t/-16=8/-16 t=1
t=-1/2
Toronto’s largest scenery, the CN tower has had several visits throughout the years. The following table represents the number of visits throughout the years. The visits V, in thousands, and the time t, in years. During which 10 year interval did the CN tower have the most visits?
Time {0 10} {20 30} {40 50}
Visits{5000 10000}{20000 40000}{80000 160000}
AROC= y2-y1/x2-x1
AROC= 160,000-80,000/50-40
AROC= 80,000/10
AROC= 8000
Therefore, the last two intervals (10 year period) had the most visits to the CN tower.
- Convert 45 degrees to radians
- Convert 315 degrees to radians
45xπ/180 315xπ/180
= π/4 7π/4
If the Sumatra earthquake from Indonesia has a magnitude of 9.1 on the Richter scale and the Prince William Sound earthquake from Alaska has a magnitude of 9.2, compare the intensities of the two earthquakes.
Sumatra EQ Prince William Sound
R=log(I/I0) R=log(I/I0)
9.1=log(I/I0) 9.2=log(I/I0)
I0 x 109.1=I I0 x 109.2=I
I=1258925412 I=1584893192
The total number of fans who’ve gone to a Drake concert from 2010 to 2018 can be modeled by the function F(x) = 64x3+2944x2+1884x-13032 and the number of Drake concerts from 2010 to 2018 can be modeled by G(x) = 16x + 724, where x is the number of years since 2010. Use long division to average the number of fans per concert.
4x2+3x-18
Elena purchased a new car for $18,999. The yearly depreciation of the value of the car can be modelled by the equation V(t) = 18,999 (0.93)t, where V(t) is the value of the car and t is the number of years that Elena owns the car. What is the rate of change in the value of the car when the car is 5 years old.
V(t)= 18,999 (0.93)5
V(t)= 18,999 (0.695688369)
V(t)= 18,999 - 13217.38
V(t)= 5781.62/5
V(t)= 1156.324
Therefore, the rate of change in the value of the car when the car is 5 years old is $1156.32
The hottest day of the year in Santiago, Chile, on average, is January 7, when the average high temperature is 29 degrees C. The coolest day of the year has an average high temperature of 14 degrees C. Use a trigonometric function to model the temperature in Santiago, Chile, using 365 days as the length of a year.
T - Temperature d - Days
Amp = max-min/2 EofA = max+min/2
Amp = 29-14/2 EofA = 29+14/2
Amp = 7.5 EofA = 21.5
T(d) = 7.5 cos(2π/365 d) +21.5
**you use 2π/365 since you want thing the whole thing to evaluate to 2π**