Mathematics, 02.03.2020 22:46 saigeshort

The number of barrels of oil produced from North Dakota oil wells since January 2014 is estimated to be B = 29.05e⁰.⁰²¹⁴ᵗ million barrels, where is in months since January 2014.
Estimate the relative rate of change of oil production in March 2015 using the following values of Δt. Round your answers to three decimal places.
(a) Δt = 1
(b) Δt = 0.1
(c) Δt = 0.01

Answers: 3

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Answer from: asiaosterling

a) $B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t = 1$ we have the following value

$B(t+ \Delta t) = B(15+1) = B(16) = 29.05 e^{0.0214 *16}= 40.912$

And the relative change would be given by:

$\frac{B(16) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.912-40.046}{40.046}= 0.0216 = \approx 2.16 \%$

b) $B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t =0.1$ we have the following value

$B(t+ \Delta t) = B(15+0.1) = B(15.1) = 29.05 e^{0.0214 *15.1}=40.131$

And the relative change would be given by:

$\frac{B(15.1) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.131-40.046}{40.046}= 0.00214 = \approx 0.214 \%$

c) $B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t =0.1$ we have the following value

$B(t+ \Delta t) = B(15+0.01) = B(15.01) = 29.05 e^{0.0214 *15.1}=40.054$

And the relative change would be given by:

$\frac{B(15.01) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.054-40.046}{40.046}= 0.000214 = \approx 0.0214 \%$

Step-by-step explanation:

For this case we have the following function given:

$B(t) = 29.05 e^{0.0214 t}$

Where t represent the number of months since January of 2014

Part a

For this case we have the initial time at January 2014 and that represent the value of t =0.

For march of 2015 the value fo t would be t = 15

We can estimate the corresponding value of B(15) and we got:

$B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t = 1$ we have the following value

$B(t+ \Delta t) = B(15+1) = B(16) = 29.05 e^{0.0214 *16}= 40.912$

And the relative change would be given by:

$\frac{B(16) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.912-40.046}{40.046}= 0.0216 = \approx 2.16 \%$

Part b

For this case we have the initial time at January 2014 and that represent the value of t =0.

For march of 2015 the value fo t would be t = 15

We can estimate the corresponding value of B(15) and we got:

$B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t =0.1$ we have the following value

$B(t+ \Delta t) = B(15+0.1) = B(15.1) = 29.05 e^{0.0214 *15.1}=40.131$

And the relative change would be given by:

$\frac{B(15.1) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.131-40.046}{40.046}= 0.00214 = \approx 0.214 \%$

Part c

For this case we have the initial time at January 2014 and that represent the value of t =0.

For march of 2015 the value fo t would be t = 15

We can estimate the corresponding value of B(15) and we got:

$B(15)= 29.05 e^{0.0214 *15}= 40.046$

For $\Delta t =0.1$ we have the following value

$B(t+ \Delta t) = B(15+0.01) = B(15.01) = 29.05 e^{0.0214 *15.1}=40.054$

And the relative change would be given by:

$\frac{B(15.01) - B(15)}{B(15)}$

And replacing we got:

$\frac{40.054-40.046}{40.046}= 0.000214 = \approx 0.0214 \%$

Answer from: Quest

idk

step-by-step explanation:

Answer from: Quest

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )
Ineed as soon as possible ! what is the approximate length of the minor arc de

Ineed as soon as possible ! what is the approximate length of the minor arc de

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The number of barrels of oil produced from North Dakota oil wells since January 2014 is estimated to...