Question

At the beginning of a population study of bees, a colony had 56,285 bees. The beepopulation decreases by 2.8% yearly. Let t be the number of years since the start of thestudy. Let y be the population of bees.Which exponential function shows the relationship between y and t?A.) y(t) = 56,285 (0.972)B.) y(t) = 1.028(56,285)'C.) y(t) = 0.972(56,285)D.) y(+) =56,285(1.028)'

Answer 1

The equation for the function is

y = a ( 1-r) ^x since we know that the function is decreasing

a is the inital amount and b is the percent that it decreases in decimal form

y = 56285 (1-.028) ^x

y = 56285 (.972)^x

We can change the variable to t since we are using time

y(t) = 56285 (.972)^t