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$</span><span class="mn">54.5</span>billionin 2013to<span class="mo">$</span><span class="mn">74.6</span>billion1in 2015. Find an exponential function to model the revenue as a function of years since 2013. What is the continuous percent growth rate, per year, of revenue? Round your answer to three decimal places. </p> <p>A(t)=? </p> <p> </p> <p>The XXXX XXX XXXXXXXXXXX XXXXXXXXX XX: X(t) = X * e^(r * t) </p> <p>We XXXX XXXX the XXXXXX XX these XXXXXXXXX/XXXXXXXXX: X, r </p> <p>This XXXXXXXX gives XXXXXXX XXXXXXXXXX. The <b>initial year, t<XXX>0</XXX> = 0</b> (XXXX XXXXXXXXXXX to XXXX), XXX the <b>initial XXXXXXX A(t<sub>0</sub>) = A(0) = XX.5 XXXXXXX</b>. </p> <p>XX XXX these XXXXXXX conditions XX solve XXX XXX constant <b>X</b>: </p> <ol><li>Plug in 0 XXX t : X(0) <ol><li>We XXX the XXXXXXX XXXX A(t) = X * e^(r * t) </li><li> X(<b>0</b>) = X * e^(r * <b>X</b>) </li><li> X(<b>0</b>) = X * e^0 </li><li> A(<b>0</b>) = P * X </li><li> X(<b>0</b>) = P </li></ol></li><li>XX know, from earlier, that X(X) = XX.5 billion </li><li>We XXX XXXX two ways to XXXXXXXXX X(0) <ol><li>X(X) = P </li><li>X(0) = XX.5 </li></ol></li><li>XXXX X = 54.5 </li></ol> <p>XXX that XX XXXX XXXX X is, all we need XX XXXX XX r. </p> <p>We XXXXX XXXX X(t) =<b> X</b> * e^(r * t). Lets XXXXXX it with XXX value XX P we XXXX XXXXX. </p> <p> A(t) = <b>(54.X)</b> * e^(r * t) </p> <p> </p> <p>XXX there is another condition XXXX XX XXXXX: XX 2015, XXXXX XXXX $XX.6 XXXXXXX. XXX t = X (XXXXXXXXXXX to 2015, 2 years after 2013), then X(2) = 74.6 XXXXXXX. </p> <p>Lets use XXXX XX XXXXX XXX r: </p> <ol><li>Plug in 2 XXX t : X(X) <ol><li>XX use X(t) = (54.X) * e^(r * t) </li><li> X(<b>X</b>) = (54.5) * e^(r * <b>X</b>) </li><li> A(X) = (XX.5) * e^(XX) </li></ol></li><li>We also know XXXX earlier XXXX X(2) = 74.6 billion </li><li>XX now know two ways to represent A(2) <ol><li>X(2) = (54.X) * e^(XX) </li><li>X(X) = XX.X XXXXXXX </li></ol></li><li>XXXX 74.X = (54.5) * e^(XX) </li><li>XXXXX for r <ol><li>XX.X = (XX.5) * e^(XX) </li><li>/54.X = /54.X </li><li>(XX.X/XX.X) = e^(2r) </li><li>ln( XX.6/XX.X ) = ln( e^(XX) ) </li><li>ln( 74.X/54.5 ) = XX </li><li>/X = /2 </li><li>XX( XX.6/XX.5 )/X = r </li></ol></li><li>XXXX r = ln( 74.6/XX.5 )/X = 0.15696990277 </li></ol> <p>This XXXXXXXX<b> r,</b> represents XXX XXXXXXXXXX growth XXXX per year of XXXXXXX. We XXXXXXX XX percentage, 15.696990277 % and then round to XXXXX decimal places: XX.X%. </p> <p>XXXX we XXXX <b>A(t) = 54.X e^(0.XXX t)</b>. </p> <p>Please XXX me XXXX XX you have any XXXXX XXXXXXXXX 😊 Good XXXX! </p> <ul><li>-Connor XXXXX </li></ul> <p> </p>">
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