Question

Help with Exponential Growth

Answer 1

so intial cost would be 30000?

Answer 2

hmm that easy you just plug in the values

Answer 3

yes it appears so

Answer 4

so then V(12)=30000e^12b

Answer 5

so the rate how would you find that?

Answer 6

hmm let me i haven't read carefully the problem

Answer 7

v(5)=v0e^(5b)
solve for b

Answer 8

the v(5) is given to you

Answer 9

v0 is the initial cost which is 30000
v(5) is the cost after five years

Answer 10

the only unknown you have there is b

Answer 11

once you found b you can finally look for v(12)

Answer 12

ohhhh
thank you

Answer 13

eh don't use 30000
in the equation you will get a wrong answer

Answer 14

so here would be 12000?

Answer 15

because the model is already in thousands

Answer 16

yeah v(5)=12 in thousands

Answer 17

do you get it

Answer 18

wait so it would just be 12?

Answer 19

correct, since the model is in thousands already

Answer 20

if you use 12000 and 30000 you will get a wrong b

Answer 21

you can try and see for yourself

Answer 22

V(5)=12e^5b
So we have to take the natural log of both sides right?

Answer 23

no v(5)=12
remember v0=30

Answer 24

you set it the wrong way

Answer 25

so just 12?

Answer 26

erggg

Answer 27

how do we solve for b then?

Answer 28

\(\large v(5)=v_0e^{5b} \Longrightarrow 12=30e^{5b}\)

Answer 29

do you see it now

Answer 30

ohhh so basically the cost difference in the 5 years

Answer 31

so would we divide 30 by both sides to start?

Answer 32

chu there?

Answer 33

yes

Answer 34

sorry i was away

Answer 35

aha its fine :p

Answer 36

that is easy to solve now!
just divide both side by 30 reduce the lHS fraction and apply ln

Answer 37

ok so .4=e^5b

Answer 38

now about this how would you go about getting the exponent alone

Answer 39

eh reduce the fraction i said not a decimal

Answer 40

never go to decimal is they didn't ask you

Answer 41

ohhh
sorry it says nearest hundred :p

Answer 42

that would be b not that fraction

Answer 43

ohhh

Answer 44

you will get a slightly wrong answer if you round before you reach the answer

Answer 45

but should i keep .4 though

Answer 46

hmm eh if you want to use then go for it!
my way is to just reduce the fraction and then apply ln

Answer 47

2/5 is the reduced fraction

Answer 48

alright

Answer 49

\(\Large 2/5=e^{5b} \Longrightarrow \ln(2/5)=5b\)

Answer 50

well it appears that won't change anything in this case just go ahead and use 0.4

Answer 51

yeh i just saw that lool

Answer 52

-.91629073

Answer 53

hmm divide by 5

Answer 54

and round the nearest hundred

Answer 55

-.18

Answer 56

hmm sounds good

Answer 57

so now we fill this in for b in the 12 year equation

Answer 58

-18/10=-9/5=b

Answer 59

yes!

Answer 60

use b to find v(t=12)

Answer 61

oks V(12)=30000e^12(-.18)

Answer 62

I said use 30 only for 30000

Answer 63

Yes i forgot T_T

Answer 64

oopsie

Answer 65

that's okay

Answer 66

V(12)=30e^12(-.18) fixed

Answer 67

okay that's good! now compute that

Answer 68

oks so 30(.11532512

Answer 69

just do the entire thing! it is just calculator work now

Answer 70

lelel sorry i like writing out steps

Answer 71

once you finished multiply by 1000 to get the answer you are looking for

Answer 72

3.46

Answer 73

3460?

Answer 74

apparently this how your function is acting