<PRE><B>Question 69849</B>
For the function defined by f(x)=5x-5, find a formula for f-^1(x
y=5x-5
Interchange x and y to get:
x=5y-5
Solve for y:
y=(1/5)x+1
That is f^-1
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Solve the equation 4^2x+1=2^3x+6.
Is that 16x+1=8x+6  ?
or is it
4^(2x)+1 = 2^(3x)+6 ?
???
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Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=2, that passes through the point P(1,4).
Form: y=ab^x+c
If y-intercept=2 then y=a+2
If horizontal asymptote is y=2 then c=2
If Passes through point (1,4) then 4=ab+2; ab=2
EQUATION: y=2^x + 2
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A bacteria culture started with a count of 480 at 8:00 a.m. and after t hours is expected to grow to f(t)=480(3/2)t. Estimate the number of bacteria in the culture at noon the same day.

8 to noon is 4 hour
Let t=4 in your equation
f(4)=480(3/2)^4
f(4)=2430
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If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate of 6% per year, then its value t years after the purchase will be f(t)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years 2005 and 2008?
In 1998 you have the value; that is when t=0
In 2005 t=2005-1998=7; find f(7)
In 2008 t=2008-1998=10; find f(10)
Subtract f(7) from f(10) to get the increase over that period.
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For the function defined by f(x)=2-x^2, 0 &lt; x, use a sketch to help find a formula for f-^1(x). 
Sketch or graph the given function.
Draw the line y=x on the same coordinate system
Sketch the curve symetric to the given curve relative to the line y=x.
For example if you have the point (0,1) in the 1st curve you want the
point (1,0) in the inverse function curve.  What you are doing is really
interchange x and y in all the points.

That is the curve of f^-1(x)
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The amount of a radioactive tracer remaining after t days is given by A=Ao e^-0.058t, where Ao is the starting amount at the beginning of the time period. How many days will it take for one half of the original amount to decay?
You want A=(1/2)Ao
You get:
(1/2)Ao=Aoe^(-0.58t)
1/2=e^(-0.58t)
Take the natural log to get:
ln(1/2) = -0.58t
Solve for t.
Cheers,
Stan H.
 
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