## neverforgetvivistee Group Title Exponential growth and decay: what exactly does 0<b<1mean? does this mean that b is a decimal? 2 years ago 2 years ago

1. TBates Group Title

It does

2. satellite73 Group Title

no it means that b is between 0 and 1

3. lilg132 Group Title

which means it has to be a decimal

4. lilg132 Group Title

you cant have a whole number between 0 and 1

5. slaaibak Group Title

lol

6. satellite73 Group Title

really? like for example 3.14?

7. lilg132 Group Title

how is 3.14 smaller then 1 and larger then 0?

8. neverforgetvivistee Group Title

and i don't really understand how the graph is supposed to be, how is it different from b > 1

9. Geometry_Hater Group Title

no it has to be between 01 and 1

10. satellite73 Group Title

or perhaps the decimal $\frac{1}{3}$

11. TBates Group Title

I suppose it has to be of the form 1/a where a>1

12. Geometry_Hater Group Title

0 and 1 i meant

13. satellite73 Group Title

point i was making is that 3.14 is a "decimal" but it is not less than 1 for that matter so is the decimal 100

14. TBates Group Title

But to get back to the actual question: if 0<b<1 then you have exponential decay: |dw:1322013206618:dw| If b>1 you have exponential growth: |dw:1322013236762:dw|

15. neverforgetvivistee Group Title

is it like 0. then whatever number?

16. satellite73 Group Title

0<b<1 means just what it says. that b is between 0 and 1. it may be represented by a decimal, or a fraction or maybe an irrational number like $\ln(2)$

17. neverforgetvivistee Group Title

oh so reading from left to right

18. slaaibak Group Title

satellite, the 3.14 logic is flawed. the relevance of 3.14 being decimal has nothing to do with 0<b<1. but I understand your point on the fractions and logarithmic functions

19. satellite73 Group Title

"decimal " is not a synonym for numbers between 0 and 1. decimal just means base ten representation

20. neverforgetvivistee Group Title

so the decimal has to be 0.whatever number?

21. neverforgetvivistee Group Title

like 0.8 or 0.08302

22. satellite73 Group Title

no 5 is a decimal, 19.95 is a decimal

23. neverforgetvivistee Group Title

for the 0<b<1

24. neverforgetvivistee Group Title

are you there?

25. slaaibak Group Title

I know. but the existence of a decimal larger than 1 does not influence the existence of a decimal less than 1 and greater than 0. just read your previous message about 3.14 closely. although this is a useless debate, the definition of a decimal was just misinterpreted and I agree with you on 0<b<1 not necessarily being decimal

26. neverforgetvivistee Group Title

but what kind of decimal does it have to be? something like 0.3 and 0.30823 or something like that?

27. slaaibak Group Title

in base 10, yes. anything like 0.05878 or 0.99 or w/e. just less than 1 and more than 0

28. neverforgetvivistee Group Title

ok thanks to all of you who answered it's clear now