word problem help

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milanna

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The function f(x) = 1 + 1.6ln(x+1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After how many consecutive days of two-hour practices can the basketball player make an average of 10 consecutive free throws.


x= number of consecutive days player practiced for 2 hours


I'm so lost on this one, this is a far as I can get. I don't even know what else I could define. Thanks.
 
G'day, Milanna.

x= number of consecutive days player practiced for 2 hours

f(x) = 1 + 1.6ln(x+1) gives the average number of consecutive free-throws in a practise.

"After how many consecutive days of two-hour practices can the basketball player make an average of 10 consecutive free throws."

After how many consecutive 2-hour practises, ie. for what value(s) of x, can the average number of free-throws in a practise be 10, that is f(x) = 1 + 1.6ln(x+1) = 10.

So after all that kerfuffle the equation is

10 = 1 + 1.6ln(x+1)

Solve for x. Remember that the exponential base e, e^(), 'undoes' a natural log, ln().
 
then for the equation

10 = 1 + 1.6ln(x+1)

I subtract 1 from both sides

9 = 1.6ln(x+1)

but then what do I do with the (x+1) ?
 
\(\displaystyle \L 9 \, = \, 1.6\ln(x \, + \, 1)\)

Divide both sides by 1.6

\(\displaystyle \L \frac{9}{1.6} \, = \, \ln{(x \, + \, 1)}\)

Take the exponential base e of both sides

\(\displaystyle \L e^{(\frac{9}{1.6})} \, = \, x \, + \, 1\)

etc.
 
I'm confused, the answers I can choose from are:

967 days
276 days
969 days
278 days
 
That's the problem, it doesn't look like I will get anything looking like those numbers.

From what I'm understanding I now have

e^5.625 = x + 1

but I don't know how to get a whole number out of that.
 
milanna said:
I now have e<sup>5.625</sup> = x + 1, but I don't know how to get a whole number out of that.
Click to expand...
Subtract the 1, and plug the thing into your calculator.

Eliz.
 
ahhh,
I got it now

2.7182818^(5.625) = x + 1

277.27 = x + 1

276.27 = x

thanks everyone :D
 
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