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 the biologist how she can solve this on a graph using a system of equation
Explain the biologist how she can solve this on a graph using a system of equation
1 answer:
This equation can be solved graphically by plotting the equations
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
_____
On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
_____
On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
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ANSWER
Vertical shift: 6 units up
Maximum value: 9
Minimum value: 3
EXPLANATION
The given since function is
Expand and rewrite to obtain,
Or
The vertical shift is 6 units up.
The maximum value is 6+3=9.
The minimum value is -3+6=3