Can anyone help me with this question please!???!??

initial population : 89

after 9 years : 676

Step-by-step explanation:

no need for panic. this is just plain calculator mechanics. yes, we need to do some more complicated typing and use e, but it is still only typing.

the initial population is P(0). or t = 0.

simply when there were 0 years since the fish were added.

that is simple.

we get (as -0.42×0 = 0)

800 / (1 + 8e⁰) = 800 / (1+8×1) = 800 / 9 ≈ 89

now, after 9 years we have to calculate P(9). or t=9.

let's pre-calculate : -0.42×9 = -3.78

e to the power of -3.78 = 0.022822691...

8 times this is 0.182581531...

and plus 1 is 1.182581531...

800 / 1.182581531... = 676.486127 ≈ 676

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

your question is incomplete, write all the numbers in the sequence that it tells you.  

step-by-step explanation: