Question

The amount of money spent for music services t years after 2010 can be approximated by m(t) = 0.54t+0.536, where m(t) is in billions of dollars. Determine (using an

inequality) those years for which more than $2 billion will be spent for music services.

Answer 1

From 2013, more than $2 billion will be spent for streaming music services

Solution:

Given that,

The amount of money spent for music services t years after 2010 can be approximated by:

m(t) = 0.54t + 0.536

where m(t) is in billions of dollars

For those years for which more than $2 billion will be spent for music services, write inequality as:

0.54t + 0.536 > 2

Solve the inequality,

`\mathrm{Multiply\:both\:sides\:by\:}1000\\\\0.54t\cdot \:1000+0.536\cdot \:1000>2\cdot \:1000\\\\540t+536>2000\\\\\mathrm{Subtract\:}536\mathrm{\:from\:both\:sides}\\\\540t+536-536>2000-536\\\\\mathrm{Simplify}\\\\540t>1464\\\\\mathrm{Divide\:both\:sides\:by\:}540\\\\(540t)/(540)>(1464)/(540)\\\\\mathrm{Simplify}\\\\t>(122)/(45)\\\\t > 2.71`

Thus, approximately after 3 years, $2 billion will be spent for music services

Thus, ( 2010 + 3 = 2013 ) from 2013, more than $2 billion will be spent for streaming music services