00:01
In this problem, we're looking at the length of some fish is modeled by this growth function here, which is given to be l of t equals to 200 times 1 minus .956e to the minus .18.
00:12
So where l of t is the length in centimeters and t is the number of years that fish is old.
00:19
The first question is what is the length of the newborn hallibut at the time of birth? so with this function here, you can actually estimate at t's equal to zero if you substitute the value of t equal to zero in this equation here you would find l of zero which means that at t equal zero you get 8 .8 .8 that would be 8 .8 centimeters that would be answered the first question.
00:42
So this is 8 .8 centimeters.
00:47
The second part is use the formula to estimate the length of five year old around your answers to two decimal places.
00:54
The five year old would be l of five.
00:57
So t equal to 5 which means that e to the minus 1 .8 .8 times 5.
01:02
So that would essentially will give rise to l of 5 equals to 122 .26.
01:10
So that would be this answer here, 122 .26 centimeters.
01:17
Finally, the third part is asking us to find out at what age would the halibut be 110 centimeters long? in this case, they've given us the length.
01:26
So which means 100.
01:27
10 will be equal to 200 times this function here and we are supposed to be finding the value of t.
01:32
So, um, rearranging the function for t, you would get 110 by 200 equals 1 minus this whole thing here, which would be 110 by 200 minus 1 equals to this part.
01:45
Therefore you can say 110 by 210 by 200 minus 0 .956 equals to each to the minus 1 .18...