Respuesta :
Answer:
Answer is f(x)=245(4^1/12)^12x
Step-by-step explanation:
The general formula for the growth of population in years is:
f(x) =P0(1+r)^x
where 1+r is the rate of growth in this case 4 and x is time in years. To take it to months we do not change initial population , this doesn't vary by changing time scale (there are 45 fruit flies in time 0 )
we change the time period x to 12 x because we want our formula to remain equivalent to the original one so if x = 1 year in months this would be equivalent to twelve months (12x = 12 with x =1 ) taht is the same
However we need to reescale our growth rate to a value that calculates it by month growth. After 12 time periods of a month our grow rate should be equivalent to the growth rate of a year. So For that reason we elevate to a 1/12 because of exponent rules
(4^1/12)^12x =(4^12x/12) because of exponent of an exponent is multiplying exponents
= (4)^x we arrive to the same expression. So
Answer:
Answer is f(x)=245(4^1/12)^12x
Step-by-step explanation:
The general formula for the growth of population in years is:
f(x) =P0(1+r)^x
where 1+r is the rate of growth in this case 4 and x is time in years. To take it to months we do not change initial population , this doesn't vary by changing time scale (there are 45 fruit flies in time 0 )
we change the time period x to 12 x because we want our formula to remain equivalent to the original one so if x = 1 year in months this would be equivalent to twelve months (12x = 12 with x =1 ) taht is the same
However we need to reescale our growth rate to a value that calculates it by month growth. After 12 time periods of a month our grow rate should be equivalent to the growth rate of a year. So For that reason we elevate to a 1/12 because of exponent rules
(4^1/12)^12x =(4^12x/12) because of exponent of an exponent is multiplying exponents
= (4)^x
