During testing of a certain brand of air purifier, the amount of smoke remaining

Question

During testing of a certain brand of air purifier, the amount of smoke remaining (as a percent of the original amount) t min after the start of the test was given by the following function.

A(t) = -0.00006t5 + 0.00468t4 - 0.1148t3 + 1.564t2 - 17.63t + 110

A''(10) =HOW DO I FIND THIS?

QUESTON #2

The median age (in years) of the U.S. population over the decades from 1960 through 2010 is given by

f(t) = 0.2176t3 + 1.962t2 2.833t + 29.4    (0 t 5)

where t is measured in decades, with

t = 0

corresponding to 1960.† (Round your answers to one decimal place.)

(a) What was the median age of the population in the year 1970?

HOW DO I FIND THIS?

Explanation / Answer

1) A(t) = -0.00006t5 + 0.00468t4 - 0.1148t3 + 1.564t2 - 17.63t + 110

A '(t) = -0.00006(5t4) + 0.00468(4t3) - 0.1148(3t2) + 1.564(2t) - 17.63          since d/dx xn = xn+1/(n+1)

A ''(t) = -0.00006(5)(4t3) + 0.00468(4)(3t2) - 0.1148(3)(2t) + 1.564(2)

A ''(10) = -0.00006(5)(4(10)3) + 0.00468(4)(3(10)2) - 0.1148(3)(2)(10) + 1.564(2)

==> A ''(10) = 0.656

2) f(t) = 0.2176t3 + 1.962t2 2.833t + 29.4

1970 ==> t = 1

==> f(1) = 0.2176(1)3 + 1.962(1)2 2.833(1) + 29.4

==> f(1) = 0.2176 + 1.962 2.833 + 29.4

==> f(1) = 0.2176 + 1.962 2.833 + 29.4

==> f(1) = 28.3114

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