Question

The current exponential function P(x)=100*2^X measures the fish population’s growth monthly. Using complete sentences explain how to find the rate of growth every week.

Answer 1

@amistre64

Answer 2

there are 4 weeks in a month .....

Answer 3

yeah

Answer 4

since 1x = 1 month
x/4 = 1 week

Answer 5

P(x)=100*2^X is per month

P(x)=100*2^(X/4) is per week

Answer 6

2x no?

Answer 7

oh i see so so how do i explain im going to find the weekly rate

Answer 8

i would try to do something like:

x = 1 month, 1 week = x/4

let w = x/4

P(w) = 100*2^w = 100*2^(x/4)

Answer 9

of course ive never been good at "explaining" in words :/

Answer 10

Thats not a problem. :) this is another part to the question The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500.

Answer 11

plug it in

500 = 100 * 2^x

divide and log if need be

Answer 12

ok so minus 100 right?

Answer 13

divide ..

Answer 14

500 = 100 * 2^x
/100 /100
----------------
5 = 2^x

Answer 15

if we divide it would be 5=2^x

Answer 16

god you were faste

Answer 17

lol .. now log off the 2

Answer 18

log(5)=(log)2^2

Answer 19

ln(5) = ln(2^x)

ln(5) = x ln(2)

ln(5)/ln(2) = x

Answer 20

in why not log

Answer 21

log is fine, works out for any base you want to apply; ln was simpler to type than log

Answer 22

so that would be the final answer or i have to press equal on the calculator lol

Answer 23

pressing equals would give us: x = 2.3219 months

you can then rework that into days, weeks, or whatever is needed

Answer 24

oh ok i can do that last part The computer system you need to input the function into only works in logarithms of base 10. Using complete sentences, explain how to convert your exponential function P(x) in a logarithmic one and then into a base 10 logarithm.

Answer 25

i got no good bead on that one ... jumping in would be about as best i could accomplish

log both sides and see if you can work out a P maybe?

Answer 26

both sides? lol i didnt even know there were sides

Answer 27

P = 100 * 2^x

log(P) = log(100 * 2^x)

log(P) = log(100) + log(2^x)

log(P) = log(100) + x log(2)

log(P) = log(10^2) + x log(2)

log(P) = 2 log(10) + x log(2)

log(P) = 2 + x log(2)

im not sure what it means to convert it into a log

Answer 28

if we wanted to find the inverse .. solving for x, we would do that process, but im not sure what it means to convert P into a log

Answer 29

ok ill turn this in to the teacher and ill tell him that too! Thank You!

Answer 30

good luck :)

Answer 31

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