In this lesson, we will learn how to solve real-world problems involving exponential functions.

Q1:

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

What was the population when the chemical was first applied?

What is the rate of population decrease?

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?

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 π percentage as a function of the concentration π in molars (M) does NOT correspond to the graph?

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

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