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#1 2021-05-02 07:27:36

mathland
Banned
Registered: 2021-03-25
Posts: 438

Restaurant

A restaurant in Naples, Florida is very busy
during the winter months and extremely slow over the summer.
But every year the restaurant grows its sales. Suppose over the
next two years, the revenue R, in units of $10,000, is projected to
follow the model R = R(t) = sin t + 0.3t + 1 0 ≤ t ≤ 12
where t = 0 corresponds to November 1, 2014; t = 1 corresponds
to January 1, 2015; t = 2 corresponds to March 1, 2015;
and so on.

(a) What is the projected revenue for November 1, 2014;
March 1, 2015; September 1, 2015; and January 1, 2016?

(b) What is the rate of change of revenue with respect to time?

(c) What is the rate of change of revenue with respect to time for
January 1, 2016?

I need steps for (a) through (c). I will do the math work.

Thanks.

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#2 2021-05-02 07:43:06

zetafunc
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Registered: 2014-05-21
Posts: 2,326
Website

Re: Restaurant

For part (a), what is the value of t for the range of dates you've given?

For part (b), you want to calculate the rate of change of R(t) with respect to t. In other words, you'll need to determine R'(t).

Part (c) just involves calculating R'(t) at that particular value of t.

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#3 2021-05-03 09:22:58

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Restaurant

zetafunc wrote:

For part (a), what is the value of t for the range of dates you've given?

For part (b), you want to calculate the rate of change of R(t) with respect to t. In other words, you'll need to determine R'(t).

Part (c) just involves calculating R'(t) at that particular value of t.

For part (a), I must evaluate R(t) at t = 1 and t = 2.  Yes?

For part (b), I get R'(t) = cos (t) + 0.3.

For part (c), what particular value of t are you taking about?

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#4 2021-05-03 11:00:59

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,326
Website

Re: Restaurant

mathland wrote:

For part (a), I must evaluate R(t) at t = 1 and t = 2.  Yes?

No. You have been given four dates, not two -- so what are the values of t at these dates?

mathland wrote:

For part (b), I get R'(t) = cos (t) + 0.3.

Correct.

mathland wrote:

For part (c), what particular value of t are you taking about?

The value of t that is mentioned in the question.

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#5 2021-05-03 11:27:10

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Restaurant

zetafunc wrote:
mathland wrote:

For part (a), I must evaluate R(t) at t = 1 and t = 2.  Yes?

No. You have been given four dates, not two -- so what are the values of t at these dates?

mathland wrote:

For part (b), I get R'(t) = cos (t) + 0.3.

Correct.

mathland wrote:

For part (c), what particular value of t are you taking about?

The value of t that is mentioned in the question.

1. I don't know the value of t for September 1, 2015; and January 1, 2016.
I can't seem to figure it out based on the given information. 

2. I don't know the value of t for January 1, 2016.

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#6 2021-05-03 19:24:05

Bob
Administrator
Registered: 2010-06-20
Posts: 9,128

Re: Restaurant

where t = 0 corresponds to November 1, 2014; t = 1 corresponds
to January 1, 2015; t = 2 corresponds to March 1, 2015;
and so on.

So each time t increases by 1, add two months to the date.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#7 2021-05-04 01:42:04

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Restaurant

Bob wrote:

where t = 0 corresponds to November 1, 2014; t = 1 corresponds
to January 1, 2015; t = 2 corresponds to March 1, 2015;
and so on.

So each time t increases by 1, add two months to the date.

Bob

For September 1, 2015, I got t = 5.

For January 1, 2016, I got t = 7.

Are those the correct t-values?

I see that the t-value increases by 1 every two months.

Last edited by mathland (2021-05-04 01:44:13)

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#8 2021-05-04 05:19:46

Bob
Administrator
Registered: 2010-06-20
Posts: 9,128

Re: Restaurant

Yes those are correct.

B


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#9 2021-05-04 07:45:31

mathland
Banned
Registered: 2021-03-25
Posts: 438

Re: Restaurant

Bob wrote:

Yes those are correct.

B

Very cool.

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