Question 69849This question is from textbook Algebra & Trigonometry with Geometry
: Help! Submitted these problems on Monday of thsi week and haven't receieved a response. Please help studying for final exam.
For the function defined by f(x)=5x-5, find a formula for f-^1(x).
Solve the equation 4^2x+1=2^3x+6.
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).
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.
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?
For the function defined by f(x)=2-x^2, 0 < x, use a sketch to help find a formula for f-^1(x).
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?
Thanks everyone for helping me out. God Bless, John
This question is from textbook Algebra & Trigonometry with Geometry
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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 < 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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