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Lesson: Solving Real-World Problems Involving Exponential Functions

Sample Question Videos

Worksheet • 21 Questions • 3 Videos

Q1:

A population of bacteria decreases as a result of a chemical treatment. The population 𝑑 hours after the treatment was applied can be modeled by the function 𝑃 ( 𝑑 ) , where 𝑃 ( 𝑑 ) = 6 0 0 0 Γ— ( 0 . 4 ) 𝑑 .

What was the population when the chemical was first applied?

What is the rate of population decrease?

  • A60% per hour
  • B1.4% per hour
  • C6% per hour
  • D4% per hour
  • E1.6% per hour

Q2:

Which is a higher annual rate and by how much: 1 8 . 2 % per year compounded weekly or 1 8 . 5 % per year compounded quarterly?

  • A 1 8 . 2 % weekly, better by about 0 . 1 %
  • B 1 8 . 5 % quarterly, better by about 0 . 0 1 %
  • C 1 8 . 5 % quarterly, better by about 0 . 1 %
  • D 1 8 . 5 % quarterly, better by about 1 0 %
  • E 1 8 . 2 % weekly, better by about 1 0 %

Q3:

Different solutions were prepared by pouring different amounts of a blue ink in a beaker and adding water to obtain 250 mL of solution. Using a light source and a light detector, the light transmitted through the beaker was measured as a function of the concentration of the solution. The given figure shows the corresponding data for the transmittance as a percentage. A concentration of 0 corresponds to pure water, and the measured value of light transmitted through the beaker containing only water was used as reference to work out the transmittance as a percentage.

Which of the following expressions for the transmittance 𝑇 percentage as a function of the concentration 𝑐 in molars (M) does NOT correspond to the graph?

  • A 𝑇 = 1 0 0 β‹… 𝑒 βˆ’ 0 . 1 4 4 𝑐
  • B 𝑇 = 1 0 0 β‹… 2   𝑐 l n l n 0 . 5 2
  • C 𝑇 = 1 0 0 β‹… 0 . 5 1 0 𝑐
  • D 𝑇 = 1 0 0 β‹… 2 βˆ’ 1 0 𝑐
  • E 𝑇 = 1 0 0 β‹… 𝑒 βˆ’ 6 . 9 3 𝑐

Giving your answer accurate to two significant figures, calculate the solution concentration that gives a transmittance of 6 8 % .

  • A0.056 M
  • B0.5 M
  • C0.2 M
  • D0.45 M
  • E0.04 M
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