1) There are 5040 commercial bee hives in a region threatened by African bees. Today African bees have taken over 70 hives. Experience in other areas shows that, in the absence of limiting factors, the African bees will increase the number of hives they take over by 20% each year. Make a logistic model that shows the number of hives taken over by African bees after t years. (Round r to three decimal places.)
5040/71e^(-.182t)+1
I got this part...BUT idk how to do part two?
2) Determine how long it will be before 1800 hives are affected. (Round your answer to two decimal places.)
+130555 For the second part, I think we have this
1800 = 5040 / [ 71 e^(-.182t)+1] rearrange as
71 e^(-.182t)+1 = 5040/ 1800 subtract 1 from both sides
71e^(-.182t) = [5040 - 1800] / 1800 simplify
71e^(-.182t) = 1.8 divide both sides by 71
e^(-.182t) = 1.8/ 71 take the ln of both sides
ln e^(-.182t) = ln[ 1.8 / 71 ] and we can write
-.182t ln e = ln [ 1.8/ 71] and ln e = 1 so we can ignore this....and we have
-.182t = ln [ 1.8 / 71] divide both sides by -.182
t= ln [ 1.8 / 71] / [-.182 ] = about 20.19 years
+130555 For the second part, I think we have this
1800 = 5040 / [ 71 e^(-.182t)+1] rearrange as
71 e^(-.182t)+1 = 5040/ 1800 subtract 1 from both sides
71e^(-.182t) = [5040 - 1800] / 1800 simplify
71e^(-.182t) = 1.8 divide both sides by 71
e^(-.182t) = 1.8/ 71 take the ln of both sides
ln e^(-.182t) = ln[ 1.8 / 71 ] and we can write
-.182t ln e = ln [ 1.8/ 71] and ln e = 1 so we can ignore this....and we have
-.182t = ln [ 1.8 / 71] divide both sides by -.182
t= ln [ 1.8 / 71] / [-.182 ] = about 20.19 years
