## neverforgetvivistee 4 years ago Exponential growth and decay: what exactly does 0<b<1mean? does this mean that b is a decimal?

1. TBates

It does

2. satellite73

no it means that b is between 0 and 1

3. lilg132

which means it has to be a decimal

4. lilg132

you cant have a whole number between 0 and 1

5. slaaibak

lol

6. satellite73

really? like for example 3.14?

7. lilg132

how is 3.14 smaller then 1 and larger then 0?

8. neverforgetvivistee

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

9. Geometry_Hater

no it has to be between 01 and 1

10. satellite73

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

11. TBates

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

12. Geometry_Hater

0 and 1 i meant

13. satellite73

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

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

is it like 0. then whatever number?

16. satellite73

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

oh so reading from left to right

18. slaaibak

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

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

20. neverforgetvivistee

so the decimal has to be 0.whatever number?

21. neverforgetvivistee

like 0.8 or 0.08302

22. satellite73

no 5 is a decimal, 19.95 is a decimal

23. neverforgetvivistee

for the 0<b<1

24. neverforgetvivistee

are you there?

25. slaaibak

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

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

27. slaaibak

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

28. neverforgetvivistee

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