Question

6. 0/1.25 points | Previous Answers WaneAC64.4.067. My Notes Ask Your Teacher The percentage y (of total personal consumption) an individual spends on food is approximately =35x-0.25 percentage points (6.5 s xs 17.5) y where x is the percentage the individual spends on education.t An individual finds that she is spending x7+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)-8.75x1.25x Use the chain rule to estimate how fast the percentage she spends on food is changing on September 1. (Round your answer to two decimal places.) Specify the units. percentage points per month percentage points per percent of budget on education percentage of budget on education per month months per percentage point

Answer 1

PART(a):

The given function is,

=35 0.25 5.T

plugin x value in terms of t,

y = 35(7 +0.2t)-0.25

PART(b):

y = 35(7 +0.2t)-0.25

diff wrt t using chain rule,

dy 35(-0.25) (7 0.2t)-0.25-1(7+0.2t) dt dt

dy 35(-0.25) (7 0.2t)-0.25-1 dt (0.2)

dy -1.75(7 0.2t)-1.25 dt

January 1 corresponds to t = 0,

September 1 corresponds to t = 8

dy -1.75(7 0.2(8))-1.25 dt

dy -0.118826959481 dt

rounding off to 3 decimals,

dy -0.119 dt

PART(c):

y represents percentage points

t represents time in months.

dy/dt represents percentage points/month

Hence Option(A) is the correct answer.

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