The human population of a remote island is given by the formula p=kr^t the where t is the time in years from when records were first kept and k and r are values to be determined. find these values given the following information. the population is initially 1000. the population is 1200 after one year. what is the population after 10 years?

Part 1)

Part 2) The population after 10 years is about 6,192 humans

Step-by-step explanation:

Part 1) Find the values of k and r

Let

p ----> the human population of a remote island

t ----> the time in years

we have

This is a exponential function of the form

where

a is the initial value or y-intercept

b is the base of the exponential function

In this problem

The initial population is 1,000

so

Remember that

the population is 1200 after one year

we have the ordered pair (1,1,200)

substitute in the equation and solve for r

therefore

Part 2) What is the population after 10 years?

For x=10 years

substitute the value of x in the exponential function

therefore

The population after 10 years is about 6,192 humans

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17