Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best
2 answers:
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Answer:
a)
b) The population estimated in 2008 is of 24651.
Step-by-step explanation:
The population growth model may be given by the following exponential function:
In which P(t) is the population after t years, is the initial population and r is the growth rate.
(A.) Find a function that models the population t years after 2000 (t=0 for 2000)
We have that:
. So
(B.) Use the function from part A to estimate the fox population in the year 2008.
2008 is 8 years after 2000. So:
The population estimated in 2008 is of 24651.
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.)