An exponential model shows the growth of a towns population in years. Identify the parts: y=25,000(1+.02)^12
Does this show growth or decay?
Rate(in %):
Starting Population:
Time:
Current Population:

9514 1404 393

Step-by-step explanation:

The base of the exponent is (1 +0.02). The value 0.02 = 2% is the growth rate. It is positive, signifying a 2% rate of growth per year. (Negative values would mean decay.)

The number 25000 that multiplies the exponential term is the value of the expression when the exponent is zero. It represents the starting population.

The exponent is said to be in years, so the time is 12 years.

The current population is the value of the expression:

  25,000(1.02^12) ≈ 31,706 . . . . current population

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.