In a linear function, the number multiplying the input is the slope: the output change for one unit of input change. If the question gives an output increase and asks for an input increase, divide the output change by the slope; Desmos can solve the decimal equation. The constant term sets the starting output, but it does not add to the change.
Hints
- Hint 1
The slope tells you how much absorbance rises for each additional mole per liter of concentration. Find the number multiplying concentration in the function. How can you use that rate to relate the two increases?
- Hint 2
The intercept is the absorbance at zero concentration. It is present both before and after concentration increases, so it cancels when you compare the outputs. Don't subtract it from the absorbance increase.
Step-by-step
Use the slope to relate the changes
Step 1Read the rate in the model
The slope is the number multiplying concentration in . So each increase of mole per liter raises absorbance by units. The is the intercept, the absorbance at zero concentration. It is present before and after the change, so it does not affect the increase.
- Step 2
Write an equation for the increase
Let be the increase in concentration, measured in moles per liter. At the given rate, that increases absorbance by units. Match it to the requested absorbance increase: .
- Step 3
Solve without rounding yet
Type , then in Desmos. Comparing to zero works because the same slope applies from any starting concentration. Desmos uses as the unknown and to find its value. Under PARAMETERS, it shows moles per liter.
- Step 4
Round to the requested place
In , the digit after the hundredths place is , so round the hundredths digit up. The concentration increase is approximately moles per liter. Choice B.