Question

Naomi says she is going to study 3 hours the first day this week and then is going to add on thirty minutes each day for the next seven days. Write a recursive formula to represent Naomi's study pledge.

Answer 1

at first tell me what you think about this question, to how we solve it ?

Answer 2

I think I figured out the recursive formula. But I also realized I need and explicit formula.

Answer 3

yes, but first you need to look the question back again.

Answer 4

The recusive is\[A(n)=a _{n-1} + 0.5\]

Answer 5

the question said naomi study 3 hours daily, that means, if we take a function which discribe this, so we can write this as\[F(x)=30\]

Answer 6

It said only on the first day does she study 3 hrs

Answer 7

The second day she studies 3.5 hrs and so on

Answer 8

yes,

Answer 9

so is the formula I wrote correct

Answer 10

but you say's that also she increase time by (1/2)hrs, per day

Answer 11

how

Answer 12

i did it in minutes.

Answer 13

so its \[A(n)=180+30^{n-1}\]
sorry i wrote it wrong last time

Answer 14

So do I need to write them both in the same terms?

Answer 15

like for the recursive \[A(n)=a _{n-1}+30\]

Answer 16

ok,but
if she study
3hrs
first day, and increase the time of study
1/2hrs
per day, so nex day she study for additional (1/2)hrs, and one another next it will increase (1/2)hrs, more

Answer 17

yep

Answer 18

So 3hrs on day 1, 3.5 on day 2, 4 on day 3...

Answer 19

thanks for the help.

Answer 20

so, i can write to describe this as like a function, as\[f(x)=3+(1/2)x\]where f(x)=total time she study, and x is day after 1st day she has started study.

Answer 21

ok

Answer 22

bt wouldn't it be \[f(x)=3+(1/2)^{x}\]

Answer 23

and besides i need a formula not a function, or are they the same.

Answer 24

the formula that i think is look like that\[f(x)=3+0.5x\]
this will give you correct total time on that day,she study for, like 1st day she study for 3 hrs, so 2nd day she study for \[1+(1/2)hrs\]

Answer 25

sorry,\[3+(1/2)\]

Answer 26

ok that makes sense

Answer 27

Thanks