Analysis to obtain the function that models the polulaiton ob bees:
1) First year 9,000 bees
2) Second year: decrease 5% => 9,000 - 0.05* 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Every year the population decreases 5% => 9,000 * 0.95)^ (number of years)
4) if you call x the number of years, and f(x) the function that represents the number of bees, then: f(x) = 9,000 (0.95)^ x.
Analysis of the statements:
1) The
function f(x) = 9,000(1.05)x represents the situation.
FALSE: WE DETERMINED IT IS f(x) = 9,000 (0.95)^x
2) The function
f(x) = 9,000(0.95)x represents the situation.
TRUE: THAT IS WHAT WE OBTAINED AS CONCLUSION OF THE PREVIOUS ANALYSIS.
3) After 2 years, the farmer
can estimate that there will be about 8,120 bees remaining.
Do the math:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0,9025 = 8,122
So, the statement is TRUE
4) After 4
years, the farmer can estimate that there will be about 1,800 bees
remaining.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
So, the statement is FALSE
5) The domain values, in the context of the situation, are
limited to whole numbers.
FALSE: THE DOMAIN VALUES ARE ALL NON NEGATIVE REAL VALUES. FOR EXAMPLE THE FUNCTION IS WELL DEFINED FOR X = 5 AND HALF
6) The range values, in the context of the
situation, are limited to whole numbers.
TRUE: THERE CANNOT BE FRACTIONS OF BEES
