# Calculus

• Jan 20th 2013, 03:05 PM
chachey19
Calculus
i am in a calculus class in college and am having trouble with inputs and outputs of functions im stuck on this particular problem. Solve for the input that corresponds to the given output value. (Round answers to three decimal places when appropriate. Enter your answers as a comma-separated list. Note: Even though the question may be completed without the use of technology, the authors intend for you to complete the activity using the technology you will be using in the remainder of the course so that you become familiar with the basic functions of that technology.) (Thinking)r(x) = 3 ln(1.8)(1.8x); r(x) = 9.6, r(x) = 30
• Jan 20th 2013, 03:48 PM
richard1234
Re: Calculus
Use whatever "solve" function your calculator has.

If you have a TI calculator, it should be "nsolve," and the general syntax is

nsolve (Equation, variable, initial guess).
• Jan 20th 2013, 04:12 PM
Soroban
Re: Calculus
Hello, chachey19!

All you need is some algebra . . .

Quote:

$r(x) \:=\:3\ln(1.8)(1.8^x)$

$\text{(a) Given: }\,r(x) = 9.6,\,\text{ find }x.$
$\text{(b) Given: }r(x) = 30,\,\text{ find }x.$

. . . $\text{Round to 3 decimal places.}$

We have: . $3\ln(1.8)(1.8)^x \;=\;r$

. . . . . . . . . . $3\ln(1.8)^{x+1} \;=\;r$

Divide by 3: . . $\ln(1.8)^{x+1} \;=\;\frac{r}{3}$

. . . . . . . . $(x+1)\ln(1.8) \;=\;\frac{r}{3}$

. . . . . . . . . . . . . . $x+1 \;=\;\frac{r}{3\ln(1.8)}$

. . . . . . . . . . . . . . . . . $x \;=\;\frac{r}{3\ln(1.8)} - 1$

Now insert a value for $r.$