Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3], (ii)[1,2], (iii)[1,-1], (iv) [1,1.2], (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)).
begin (array)(|c|c|c|c|c|c|) hline interval & [1,3] & [1,2] & [1,-1] & [1,1.2] & [1,1.1] hline average rate of change & & & & & hline end (array)
Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.

Question

Let f(x) = 3^x. Tabulate the change of f over the intervals (i) [1,3],      (ii)[1,2],      (iii)[1,-1],      (iv) [1,1.2],      (v)[1,1.1], (vi)[1,1.01]. Graph y = 3^x together with the secant line passing through (1,f(1)) and (1.1, f(1.1)).
begin (array)(|c|c|c|c|c|c|) hline interval & [1,3] & [1,2] & [1,-1] & [1,1.2] & [1,1.1]   hline average rate of change & & & & &   hline end (array)
Based on the pattern of numbers (without deriving a general formula), estimate how quickly f(x) = 3^x changes at x = 1.