## anonymous 4 years ago Exponential Growth problem...see attached. I got r = .014384, but the answer key says otherwise.

1. anonymous

i got a cartoon and some cars when clicking on the link

2. anonymous
3. anonymous

How's that?

4. anonymous

ok what is "growth constant?" are you supposed to find k in $Ae^kt$?

5. anonymous

i meant $P(t)=A_0 e^{kt}$

6. anonymous

that's the formula that I used. I used 4.5 for A0

7. anonymous

20 for time since 1980

8. anonymous

6 on the other side

9. anonymous

ok so you should be solving $6=4.5e^{20k}$ for k

10. anonymous

yes

11. anonymous

I divided both sides by 4.5, then took the natural log of both sides

12. anonymous

I got .28768 = 20 k

13. anonymous

$\frac{6}{4.5}=e^{20k}$ $\frac{4}{3}=e^{20k}$ $20k=\ln(\frac{4}{3})$ $k=\frac{\ln(\frac{4}{3})}{20}$

14. anonymous

solving for k, I got .014384

15. anonymous

16. anonymous

$k=0.0143841$ rounded

17. anonymous

i get what you got

18. anonymous

I don't know where they are getting this answer from in the key....must be a typo?

19. anonymous

20. anonymous

lol, thanks for checking with me

21. anonymous

it happens. problems written my cadres of bored graduate students for extra cash, can easily be a mistake