A biologist cultures a strain of bacteria whose population P(t) (in thousands of cells) satisfies dtdP=kP. The initial instrument reading shows 4.00 (thousand cells) at t=0. A second reading, taken 3.00\,h later, shows 4.80. Each instrument reading is subject to a possible error of ±2%.
(a) Using the stated measurement uncertainties, determine the interval of possible values for the growth constant k (in h−1). Express your answer as an inequality.
(b) Using the nominal measurements (4.00 and 4.80), compute the predicted population after 8.00\,h, rounded to the nearest hundred cells.
(c) Explain how the uncertainty in part (a) affects the reliability of the prediction found in part (b).