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anonymous
 one year ago
A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 3^x = 5x − 1.
Explain to the biologist how she can solve this on a graph using a system of equations.
anonymous
 one year ago
A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 3^x = 5x − 1. Explain to the biologist how she can solve this on a graph using a system of equations.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Michele_Laino please please help me or ask someone for me

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1A possible way is: I call with g(x) the function 3^x, and with g(x) the function 5x1, namely I write this: \[\Large \begin{gathered} f\left( x \right) = {3^x} \hfill \\ g\left( x \right) = 5x  1 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then I draw the graph of both functions f(x) and g(x) and I search for intersection point of those graphs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is there a way of finding the intersection without graphing

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1one point is given setting x=2 we have: \[\Large \begin{gathered} f\left( 2 \right) = {3^2} = 9 \hfill \\ g\left( 2 \right) = 5 \cdot 2  1 = 9 \hfill \\ \end{gathered} \] so the corresponding intersection point is: \[\Large \left( {2,9} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1another point can be compute, if we expand the function f(x) around x=0, using Taylor expansion

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where did you get 2 from

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I did some trial

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please wait, try to write the Taylor expansion, around, x=0 of f(x), or try to use a software online like "desmos"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hold the question says use system of equations

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! in fact I broke your equation in two functions

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1here is the system: \[\Large \left\{ \begin{gathered} f\left( x \right) = {3^x} \hfill \\ g\left( x \right) = 5x  1 \hfill \\ \end{gathered} \right.\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but there is no way of eliminating anything so is that why we graph

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1for example, I write the Taylor expansion of f(x):

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it is just that i did not learn about the taylor expansion

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1please here is the expansion up to the first order term:

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[\Large {3^x} \simeq {\left. {{3^x}} \right_{x = 0}} + {\left. {{3^x}\log 3} \right_{x = 0}}x = 1 + x\log 3\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, if we want to solve your equation, namely: 3^x=5x1, we can solve this equation: \[\Large 1 + x\log 3 = 5x  1\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we get the second intersection point

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thank you, no need to go further.
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