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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 for XXXXXXXXXXX functions is: X(t) = X * e^(r * t) </p> <p>XX must XXXX the values of these variables/constants: X, r </p> <p>This XXXXXXXX gives XXXXXXX conditions. The <b>initial year, t<XXX>0</sub> = X</b> (XXXX XXXXXXXXXXX XX 2013), and the <b>initial revenue A(t<sub>0</sub>) = A(0) = 54.5 billion</b>. </p> <p>We XXX these initial conditions XX solve XXX XXX constant <b>X</b>: </p> <ol><li>XXXX in 0 for t : X(X) <ol><li>XX XXX the general form X(t) = X * e^(r * t) </li><li> A(<b>0</b>) = P * e^(r * <b>X</b>) </li><li> X(<b>X</b>) = X * e^0 </li><li> A(<b>0</b>) = X * X </li><li> A(<b>0</b>) = P </li></ol></li><li>We know, XXXX earlier, XXXX X(0) = XX.5 billion </li><li>We XXX XXXX two ways to XXXXXXXXX X(0) <ol><li>X(X) = X </li><li>A(0) = XX.5 </li></ol></li><li>Thus X = 54.X </li></ol> <p>XXX XXXX XX know what X is, all we XXXX to XXXX XX r. </p> <p>XX XXXXX with X(t) =<b> X</b> * e^(r * t). XXXX update it with XXX XXXXX XX P XX just found. </p> <p> X(t) = <b>(XX.5)</b> * e^(r * t) </p> <p> </p> <p>Now XXXXX XX XXXXXXX XXXXXXXXX that is given: In 2015, Apple XXXX $XX.6 billion. Let t = X (corresponds XX XXXX, 2 years after XXXX), XXXX A(2) = 74.X XXXXXXX. </p> <p>XXXX use this XX XXXXX XXX r: </p> <ol><li>XXXX in 2 for t : A(2) <ol><li>XX use A(t) = (XX.5) * e^(r * t) </li><li> X(<b>2</b>) = (XX.5) * e^(r * <b>X</b>) </li><li> X(X) = (54.5) * e^(XX) </li></ol></li><li>XX XXXX know XXXX XXXXXXX XXXX A(X) = 74.6 XXXXXXX </li><li>XX XXX XXXX XXX ways XX XXXXXXXXX X(2) <ol><li>A(2) = (XX.X) * e^(XX) </li><li>X(2) = 74.X billion </li></ol></li><li>XXXX 74.X = (54.5) * e^(2r) </li><li>Solve for r <ol><li>74.X = (54.5) * e^(2r) </li><li>/54.X = /XX.5 </li><li>(74.6/54.X) = e^(XX) </li><li>XX( 74.X/XX.X ) = XX( e^(XX) ) </li><li>XX( XX.6/XX.5 ) = XX </li><li>/X = /2 </li><li>XX( XX.6/XX.X )/2 = r </li></ol></li><li>Thus r = XX( 74.6/54.5 )/X = 0.XXXXXXXXXXX </li></ol> <p>XXXX XXXXXXXX<b> r,</b> XXXXXXXXXX XXX XXXXXXXXXX growth XXXX XXX year of revenue. XX XXXXXXX XX percentage, XX.696990277 % XXX XXXX round XX three XXXXXXX places: XX.X%. </p> <p>Then we have <b>X(t) = XX.X e^(0.157 t)</b>. </p> <p>XXXXXX let me XXXX XX you have XXX other XXXXXXXXX 😊 Good luck! </p> <ul><li>-Connor Myers </li></ul> <p> </p>">
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