The populations P (in thousands) of Orlando, Florida from 2000 through 2007 can be modeled by P = 1656.2e^kt

where t represents the year, with t =0 corresponding to 2000.

In 2005, the population of Orlando was about 1,940,000. (Source: U. S. Census Bureau)

(a) Find the value of k. Is the population increasing or decreasing? Explain.

(b) Use the model to find the populations of Orlando in 2010 and 2015. Are the results reasonable? Explain.

Explained below.

Step-by-step explanation:

The population model for Orlando, Florida from 2000 through 2007 is:

It is provided that, in 2005, the population of Orlando was about 1,940,000.

(a)

Compute the value of k as follows:

For year 2005, the value of t is 5.

Since the value of k is positive, the population is increasing.

(b)

Compute the populations of Orlando in 2010 as follows:

Compute the populations of Orlando in 2015 as follows:

Since the population increased exponentially from 2010 to 2015, yes the results are reasonable.

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺