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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 is: X(t) = P * e^(r * t) </p> <p>XX must find XXX values XX XXXXX XXXXXXXXX/constants: X, r </p> <p>This question XXXXX XXXXXXX XXXXXXXXXX. XXX <b>initial year, t<XXX>X</XXX> = 0</b> (XXXX corresponds XX 2013), XXX the <b>XXXXXXX XXXXXXX X(t<sub>X</XXX>) = X(0) = XX.5 XXXXXXX</b>. </p> <p>We XXX these XXXXXXX conditions to XXXXX XXX the XXXXXXXX <b>P</b>: </p> <ol><li>Plug in 0 XXX t : X(X) <ol><li>XX use XXX general XXXX X(t) = X * e^(r * t) </li><li> A(<b>X</b>) = X * e^(r * <b>X</b>) </li><li> A(<b>0</b>) = P * e^0 </li><li> A(<b>X</b>) = P * 1 </li><li> X(<b>X</b>) = X </li></ol></li><li>We know, XXXX XXXXXXX, XXXX A(X) = XX.5 billion </li><li>XX XXX XXXX two XXXX to represent A(X) <ol><li>X(X) = X </li><li>X(X) = XX.X </li></ol></li><li>Thus P = 54.X </li></ol> <p>XXX XXXX XX XXXX what X XX, XXX XX XXXX to find XX r. </p> <p>We XXXXX XXXX X(t) =<b> X</b> * e^(r * t). Lets update it with the value of P XX just found. </p> <p> A(t) = <b>(54.X)</b> * e^(r * t) </p> <p> </p> <p>XXX there is another XXXXXXXXX XXXX is XXXXX: In 2015, XXXXX made $74.X billion. Let t = X (XXXXXXXXXXX XX XXXX, 2 XXXXX after XXXX), XXXX X(2) = 74.6 XXXXXXX. </p> <p>Lets use XXXX to XXXXX XXX r: </p> <ol><li>Plug in 2 XXX t : A(X) <ol><li>XX XXX A(t) = (XX.5) * e^(r * t) </li><li> A(<b>2</b>) = (54.5) * e^(r * <b>X</b>) </li><li> X(2) = (XX.X) * e^(XX) </li></ol></li><li>XX also XXXX from XXXXXXX that X(X) = 74.6 billion </li><li>XX XXX XXXX XXX XXXX to represent A(2) <ol><li>A(X) = (54.5) * e^(2r) </li><li>X(2) = XX.6 billion </li></ol></li><li>Thus XX.6 = (54.X) * e^(XX) </li><li>Solve for r <ol><li>74.6 = (54.X) * e^(XX) </li><li>/XX.X = /54.5 </li><li>(XX.6/54.X) = e^(XX) </li><li>ln( 74.6/XX.X ) = ln( e^(2r) ) </li><li>XX( 74.6/XX.5 ) = XX </li><li>/X = /2 </li><li>ln( XX.6/XX.X )/X = r </li></ol></li><li>Thus r = XX( 74.6/54.5 )/2 = X.XXXXXXXXXXX </li></ol> <p>This constant<b> r,</b> XXXXXXXXXX XXX XXXXXXXXXX XXXXXX rate XXX year of revenue. We XXXXXXX XX percentage, 15.696990277 % XXX XXXX round to three XXXXXXX XXXXXX: 15.7%. </p> <p>XXXX XX XXXX <b>X(t) = 54.5 e^(X.157 t)</b>. </p> <p>XXXXXX XXX me XXXX if you have any other XXXXXXXXX 😊 Good XXXX! </p> <XX><li>-XXXXXX XXXXX </li></ul> <p> </p>">
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