Sec 4 A-Math Linear Law topical questions

The variables x and y are connected by y = ax² + b. State what you should plot to obtain a straight line, and identify what the gradient and the vertical intercept of that line represent.

The variables x and y satisfy y = kbˣ. It is given that a graph of lg y against x is the line lg y = 0.30x + 0.48, and that lg 2 = 0.30 and lg 3 = 0.48. Find the values of k and b.

For the model y = 2x^1.5, complete this table of exact values: x = 1, 4, 9 give y = 2, ▢, ▢.

Points (lg x, lg y) lie on the line lg y = 2 lg x + 0.48, where lg 3 = 0.48. Find the relationship between x and y in the form y = px^q.

Experimental data for a relation y = axⁿ produce the line of best fit lg y = 1.5 lg x + 0.30, where lg 2 = 0.30. Find a and n, and write down the model connecting x and y.

For a relation y = c·dˣ, the plotted line of lg y against x passes through (0, 0.70) and (2, 1.70), where lg 5 = 0.70. Find the values of c and d, giving d correct to 3 significant figures.

A culture of bacteria is modelled by y = abˣ. Counts give (x, y) = (1, 6), (2, 18), (3, 54), (4, 162). (a) Show that these data are consistent with the model by considering lg y against x, using lg 2 = 0.30, lg 3 = 0.48. (b) Find a and b. (c) Predict y when x = 5.

The variables x and y satisfy y² = ax³ + b, where a and b are constants. (a) State what you plot to obtain a straight line and identify the gradient and intercept. (b) Given that this line has gradient 4 and vertical intercept 1, find y when x = 2, giving your answer correct to 3 significant figures.

The variables x and y satisfy y = ax + b/x, where a and b are constants. (a) Show that xy = ax² + b, and state what to plot to obtain a straight line. (b) The plotted line has gradient 2 and vertical intercept 5. Find y when x = 4.