Solve the problem.Given an algae population in a certain pond, x (in millions), f(x) models the frog population in the pond (in thousands). (i) Use the graph of f to estimate the number of algae in the pond when there are 29 thousand frogs in the pond; (ii) Estimate f(x) at 2, 3, 5, 6 and 7; (iii) Use regression and the points you estimated to find a quartic polynomial function f that models the data points; (iv) Use f(x) to solve part (i) either graphically or numerically.

Question

A. (i) about 1 million
(ii)   (approximately; answers may vary);
(iii) f(x) ? -0.18x⁴ + 3.27x³ + 20.02x² + 55.93x - 46.00;
(iv) x ? 1.1 million algae when f(x) = 29 thousand frogs
B. (i) about 1 million
(ii)   
(iii) f(x) ? 0.16x⁴ + 3.77x³ + 20.02x² + 51.93x - 44.00;
(iv) x ? 1.5 million algae when f(x) = 29 thousand frogs
C. (i) about 5 million
(ii)   (approximately; answers may vary);
(iii) f(x) ? -0.18x⁴ + 3.77x³ - 20.02x² + 41.93x - 44.00;
(iv) x ? 5.1 million algae when f(x) = 29 thousand frogs
D. (i) about 7 million
(ii)   (approximately; answers may vary);
(iii) f(x) ? -0.18x⁴ + 3.27x³ - 20.02x² + 51.93x - 44.00;
(iv) x ? 7.3 million algae when f(x) = 29 thousand frogs

Answer 1

Answer: D