A microbiologist is growing bacteria cultures in the lab. After 5 minutes, a bacteria colony has 1.3 million organisms. After 12 minutes, the same colony has 41.5 million. After 15 minutes, the colony has grown to 101.3 million organisms. Is this a proportional or non-proportional relationship?

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

just get this app called photo math it should be able to do those