Business Cal

The spot price of crude oil during the period 2000-2005 can be approximated byP(t) = 5t+ 25 dollars per barrel(0t5)in yeart, wheret= 0 represents 2000. Saudi Arabia's crude oil production over the same period can be approximated byQ(t) = 0.082t20.22t+ 8.2 million barrels per day(0t5)Use these models to estimate Saudi Arabia's daily oil revenue and also its rate of change in2005. (Round your answers to the nearest $1 million.)daily oil revenue$ 457.5millionrate of change in2005$million/yrFIND RATE change in 2005Calculate the derivative of the function. HINT [See Example 1.]f(x) = (6.4x6)2+ (4.3x4)2f '(x)=                   The percentagey(of total personal consumption) an individual spends on food is approximatelyy= 35x0.25percentage points (6.5x17.5)wherexis the percentage the individual spends on education.An individual finds that she is spendingx= 7 + 0.2tpercent of her personal consumption on education, wheretis time in months since January 1. Use direct substitution to express the percentageyas a function of timet(do not simplify the expression). (NOTE: January 1 is represented byt= 0.)y(t)=                    Use the chain rule to estimate how fast the percentage she spends on food is changing onAugust1. (Round your answer to two decimal places.)Answer:Specify the units.