Rainwater collected in a laboratory sample has a hydrogen–ion concentration that may…
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
Rainwater collected in a laboratory sample has a hydrogen–ion concentration that may vary between 10−6 mol L−1 and 10−3 mol L−1. Chemists use the quantity
p(x)=−log10(x),
where x is the hydrogen–ion concentration in moles per litre, to indicate the acidity of the water.
Answer the following with reference to the above situation.
(i) Identify the input variable and the output variable in this context. State with reason whether p associates exactly one output value with every admissible input value.
(ii) Determine the domain and the range of the function p for the given interval of concentrations.
(iii) Is it possible, under the stated physical conditions, for the value of p(x) to be negative? Justify your answer using the definition of the range obtained in part (ii).