1. The monthly earnings of a company that offers access to customizable personal

Question

1. The monthly earnings of a company that offers access to customizable personal internet radio stations to subscribers of the service has been steadily increasing over the last several months, as described by the model m(t)=50+3t+4t^(3/2), where t measures months, with t=0 corresponding to the start of 2011, and m(t) gives the corresponding monthly earnings, in thousands of dollars.

A. Calculate the rate at which monthly earnings were changing as of the start of 2012, rounded and labeled accordingly.

B. Determine the first full month when earnings were frowing at a rate of at least $24,000 per month.

2. let g(x)=|x^2-4|. Find a piecewise-defined formula for g ' (x).

Explanation / Answer

1)given

a)m(t)=50+3t+4t3/2

differentiate with respect to time t

dm/dt=0+3+4(3/2)t(3/2)-1

dm/dt=3+6t1/2

at the start of 2012 , t =12

dm/dt=3 +6*121/2

dm/dt =23.78

dm/dt =24

monthly earnings changing at 24 thousand dollars per month

b) earnings were frowing at a rate of at least $24,000 per month.

dm/dt=3+6t1/2=24

6t1/2=24-3

6t1/2=21

t1/2=21/6

t=(21/6)2

t =12.25

in the first month of 2012 earnings were frowing at a rate of at least $24,000 per month.

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