Business Cal

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Business Cal

The spot price of crude oil during the period 2000-2005 can be approximated by

P(t) = 5t + 25 dollars per barrel(0 ≤ t ≤ 5) 

in year 
t, where 
t = 0 represents 2000. Saudi Arabia’s crude oil production over the same period can be approximated by

Q(t) = 0.082t2 − 0.22t + 8.2 million barrels per day†(0 ≤ t ≤ 5) 

Use these models to estimate Saudi Arabia’s daily oil revenue and also its rate of change in 2005. (Round your answers to the nearest $1 million.)

daily oil revenue $  457.5million 
rate of change in 2005 $   million/yr 

FIND RATE change in 2005

Calculate the derivative of the function. HINT [See Example 1.]

f(x) = (6.4x − 6)−2 + (4.3x − 4)−2

f ‘(x)  = 

                                       

The percentage y (of total personal consumption) an individual spends on food is approximately

y = 35x−0.25 percentage points  (6.5 ≤ x ≤ 17.5) 

where 
x is the percentage the individual spends on education.
† An individual finds that she is spending

x = 7 + 0.2t

percent of her personal consumption on education, where 
t is time in months since January 1. Use direct substitution to express the percentage 
y as a function of time 
t (do not simplify the expression). (NOTE: January 1 is represented by 
t = 0.)

y(t)  =                                        

 

Use the chain rule to estimate how fast the percentage she spends on food is changing on August 1. (Round your answer to two decimal places.)

Answer:

Specify the units.