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help me to solve this problem

find exponential function f(x)=Ca^x with the 2 given points (0,5)(2,5/9)

find exponential function f(x)=Ca^x with the 2 given points (0,5)(2,5/9)

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- Thread starter linhthuy256
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find exponential function f(x)=Ca^x with the 2 given points (0,5)(2,5/9)

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- #2

LeonhardEuler

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Alright, [itex]f(x)=Ca^x[/itex], f(0)=5, and f(2)=5/9. So you have two equations and two unkowns: a and C. You can write the first equation as:linhthuy256 said:plz help me to solve this problem

find exponential function f(x)=Ca^x with the 2 given points (0,5)(2,5/9)

thankzzzzzzzzzz..........

[tex]5=Ca^0[/tex]

What is a number to the zero power? Answer that and you have C. Now the second equation is:

[tex]\frac{5}{9}=Ca^2[/tex]

Remember, you already found C from the last equation, so you just have to find a. Just isolate "a" and take the square root of both sides:

[tex]a=\sqrt{\frac{5}{9C}}[/tex]

Then just plug "a" and "C" back into the original equation and you're done.

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- #4

LeonhardEuler

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Have you found "a" now?

- #5

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yep a=3radical1 rite?

- #6

LeonhardEuler

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You mean [itex]a=\frac{1}{3}[/itex] right?

- #7

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- #8

LeonhardEuler

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That seems right. Try 5*(1/3)^x, with the parentheses, maybe.

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linhthuy256 said:

beside i still have 1 more problem that is really need help will u able to help me plz?

- #10

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linhthuy256 said:beside i still have 1 more problem that is really need help will u able to help me plz?

yes i did every single posible way but it stills said "wrong" or the answer is not accepted.

- #11

LeonhardEuler

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Alright, what's the other problem?linhthuy256 said:beside i still have 1 more problem that is really need help will u able to help me plz?

- #12

LeonhardEuler

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What was the exact phrasing of the problem?linhthuy256 said:yes i did every single posible way but it stills said "wrong" or the answer is not accepted.

- #13

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the exact phrasing was what i posted it on at first.

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compare the functions f(x)=x^5 and g(x)=5^x by graphing both f and g in several viewing rectangles.

a) find the x-coordinates of the point intersectionof the two curves accurate to two decimal places. and i did the graphing w/ a result of (1.70,1.70) is that rite?

and part b) find the value of x greater than 5 for which g(x)=400 f(x)

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yeah i got the first problem rite. thanks

- #16

LeonhardEuler

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No, that's not right, in fact niether function passes through that point. You could graph the two functions in a different window to find the true intersection, but it is clear by inspection that x=5 will yield 5^5 in both cases. As for the second case, just graph 400x^5 instead of x^5 and see where this intersects g(x).linhthuy256 said:

compare the functions f(x)=x^5 and g(x)=5^x by graphing both f and g in several viewing rectangles.

a) find the x-coordinates of the point intersectionof the two curves accurate to two decimal places. and i did the graphing w/ a result of (1.70,1.70) is that rite?

and part b) find the value of x greater than 5 for which g(x)=400 f(x)

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i can not find the intersection of 400x^5

- #18

LeonhardEuler

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Look between x=10 and x=12. y will be between 10^6 and 10^8.

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LeonhardEuler said:Look between x=10 and x=12. y will be between 10^6 and 10^8.

it's still have no intersection point between 10 or 12-13

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LeonhardEuler

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- #22

LeonhardEuler

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- #23

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LeonhardEuler said:

i give up i did as wat u say for both first and second curve but still it doesn't show any intersection point when i go between x=1 and up to x=25

- #24

LeonhardEuler

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I have to go to sleep now, so I hope you manage to figure this out now. If not, hopefully someone else will come. Good luck!

- #25

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ok i found 1 point that's 11.17 rite?

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