To derive the function that characterizes the bee population:
1) Initially, there are 9,000 bees in the first year.
2) In the second year, a reduction of 5% occurs => 9,000 - 0.05 * 9,000 = 9,000 * (1 - 0.05) = 9,000 * 0.95
3) Each subsequent year sees a 5% decline => 9,000 * (0.95)^(number of years)
4) Let x represent years and f(x) signify the bee count, then: f(x) = 9,000 (0.95)^x.
Evaluation of the claims:
<span>1) The function f(x) = 9,000(1.05)x applies to the scenario.
FALSE: WE ESTABLISHED IT AS f(x) = 9,000 (0.95)^x
2) The function f(x) = 9,000(0.95)x applies to the scenario.
TRUE: THIS IS THE RESULT OF OUR PRIOR ANALYSIS.
3) After 2 years, the farmer projects approximately 8,120 bees will be left.
Calculating:
f(2) = 9,000 * (0.95)^2 = 9,000 * 0.9025 = 8,122
Thus, this statement is TRUE
4) After 4 years, the farmer can predict there will be roughly 1,800 bees left.
f(4) = 9,000 * (0.95)^4 = 9,000 * 0.81450625 = 7,330
This statement is therefore FALSE
5) The domain values contextual to this situation are restricted to whole numbers.
FALSE: DOMAIN VALUES INCLUDE ALL NON-NEGATIVE REAL NUMBERS. FOR INSTANCE, THE FUNCTION IS VALID AT X = 5.5
6) The range values pertinent to this situation are restricted to whole numbers.
TRUE: FRACTIONS OF BEES CANNOT EXIST.
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Shane and Abha received a team badge for gathering at least 2000 cans for recycling.
This indicates that their collection must total a minimum of 2000 cans.
Abha managed to collect 178 more cans than Shane.
Let’s denote the number of cans Shane collected as S
So, Abha collected = S + 178
The inequality representing the number of cans collected by Shane can be expressed as:
= 
Begin by grouping the first two terms together and the last two together, then factor and redistribute
(4x^3+x^2)+(-8x-2)
(x^2)(4x+1)+(-2)(4x+1)
x^2(4x+1)-2(4x+1)
the answer is the first one
