## anonymous one year ago A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days: f(n) = 12(1.03)n Part A: When the scientist concluded his study, the height of the plant was approximately 16.13 cm. What is a reasonable domain to plot the growth function? (4 points) Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points) Part C: What is the average rate of change of the function f(n) from n = 3 to n = 10, and what does it represent? (4 points)

1. anonymous

@Michele_Laino

2. Michele_Laino

3. anonymous

alright:)

4. Michele_Laino

here I am!

5. anonymous

yay! ok so I got part B and part C. all I need is A

6. Michele_Laino

is your function like below: $\Large f\left( n \right) = 12 \cdot {1.03^n}$

7. anonymous

yes, just with parenthesis but that don't realy matter that much.

8. Michele_Laino

then we have to search for the value for n0, approximated by excess, such that: $\Large 16.13 = 12 \cdot {1.03^{{n_0}}}$

9. anonymous

ok so we will put what on both sides? ik that we have to do that.

10. Michele_Laino

hint: using decimal logarithms we can write: $\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = ...?$

11. anonymous

16.3/12=1.35/1.03=1.31 correct?

12. Michele_Laino

not exactly since we have to compute this: $\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} = \frac{{\log \left( {1.35} \right)}}{{\log \left( {1.03} \right)}} = ...?$

13. anonymous

im still getting 1.31 from 1.35/1.03...

14. Michele_Laino

please we have to comute the ratio between the logarithm of 1.31 and the logarithm of 1.03, being both logarithms are decimal logarithms

15. Michele_Laino

compute*

16. anonymous

ok so im trying to find the ratio between 1.31 and 1.03?

17. Michele_Laino

hint: using windows calculator, for example, we get this: $\Large {n_0} = \frac{{\log \left( {16.13/12} \right)}}{{\log \left( {1.03} \right)}} \cong 10$ so, a reasonable domain, it is given by the subsequent set: $\Large \left\{ {0,1,2,3,4,5,6,7,8,9,10,11} \right\}$

18. anonymous

@peachpi

19. anonymous

@Michele_Laino is that all?

20. anonymous

@peachpi what would be the domain? it don't seem exactly like the one I did with you.

21. anonymous

The domain would be the set of numbers @Michele_Laino entered, assuming they don't want to include partial day.

22. anonymous

so the domain is just those numbers? so that's what I would put.?

23. anonymous

yes. you could also say [0, 11] if you prefer a continuous function

24. anonymous

ok, well thanks. can I tag you in some other questions @peachpi ?

25. anonymous

sure, but I come and go

26. anonymous

ok.