Asymptotes & Equations
What an asymptote represents
The value a function is approaching but will never come into contact with or cross.
A population of 32,000 with a 5% annual growth rate would expect how many people after 7.5 years?
About 46,139 people
Wade bought a car for $22,499, but the value of the car decreases by 11% each year. Determine the cars value after 3 years. Set-up and solve.
$15,861.10
Base equations for compound interest and simple interest.
C=p(1+r)t
S=prt
Ms. Poppleton's preferred ice cream flavour.
Coffee (or coconut)
Draw a graph to represent y=-3(1.5)x
Asymptote: x-axis
Intercept: (0,-3)
(-1,-2)
In 1970 the population of a city was about 278,000 people. It seems to be growing at an average annual rate of 1.8%. Find the number of people who lived there in 1990 the number of people who would be living there today. (Round to the nearest whole value)
1990: 397,192 people
2024: 728,492 people
You drink a beverage with 120mg of caffeine. Each hour, the caffeine in your system decreases by 12.5%. Estimate the amount of caffeine in your system after 7 hours.
About 49 mg
$27000 compounded annually at 9.5% for 6 years. Set up and solve.
$46542.37
The table number that Ms. Poppleton sat at for the OWS auction. (1-25)
Table 2
Draw the graph of the exponential function: y=5(0.75)x - 7
Asymptote at -7, intercept at -2
Goes through: (-1, -1/3) (1, -3.25)
A flu outbreak hits your school on Monday, with an initial number of 20 ill students coming to school. The number of ill students increases by 25% per hour. Write an equation and solve for how many students would be sick after 6 hours.
About 76 students
A total of 50,000 contestants participate in an Internet on-line survivor game. The game randomly votes off 20% of the contestants each day. Write an equation and solve for how many contestants are left in the game at the end of one week?
About 10,486 people
$895 compounded monthly at 4.5% for 8 years. Set up and solve.
$1281.97
Ms. Poppleton's favourite class in school (aside from math)
Art (specifically print making or ceramics)
Write the equation for the graph:
y=6(1.5)x-3
Jake lends $20,000 to his friend compounded annually. Using the exponential growth formula, find the rate of growth if he anticipates $27,892 after 6 years. Round your answer to the nearest tenth.
About 5.7% growth
A radioactive isotope decays continuously from an initial quantity of 12,000 to 1,600 over the course of 8 days. What is the decay rate (per day) of the isotope as a percentage?
About 22.26% decrease
A compound interest account that pays 2.5% interest is worth $5519.06 after four years. Find the initial investment.
About $5000
What colour does Ms. Poppleton never use when checking work?
Red
Using systems of equations solve for the exponential function that goes through the points (2,432) and (5, 16).
y=3888(1/3)x
The initial population of a colony of bacteria in a petri dish is 1500. The colony grows at a rate of 5.7% per hour. The next observed population of the colony of bacteria was 2800. How many hours passed between observations?
About 11 hours
A population of 80 cougars decreases at a rate of 5% per year. After how many years will the population first drop below 40 cougars?
13.51 years
$2000 is invested in a compound interest account. After 5 years, it is worth $2341.15. Determine the compound interest rate.
3.2%
The last movie Ms. Poppleton watched.
Wonka