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Chapter 4: Problem 77

Use a calculator to evaluate the function at the indicated value of \(x .\) Round your result to three decimal places. (Value) $$x=11$$ $$x=18.31$$ $$x=\frac{1}{2}$$ $$x=\sqrt{0.65}$$ (Function) $$f(x)=\ln x$$

Short Answer

Expert verified
The solutions for each value of \(x\) will differ and will be accurately obtained by using a calculator to calculate the natural logarithm. The results must be rounded to three decimal places.

Step by step solution

01

Evaluate \(\ln x\) for \(x=11\)

Ensure the calculator is set in logarithmic mode, then input \(\ln 11\). Round the result to three decimal places.
02

Evaluate \(\ln x\) for \(x=18.31\)

In logarithm mode, input \(\ln 18.31\). Again, round the value to three decimal places.
03

Evaluate \(\ln x\) for \(x=0.5\)

Input this argument into the calculator and again, round the output to three decimal places.
04

Evaluate \(\ln x\) for \(x = \sqrt{0.65}\)

First, compute \(\sqrt{0.65}\) and then evaluate \(\ln x\). As earlier, round the result to three decimal places.

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Most popular questions from this chapter

Use a graphing utility to approximate the point of intersection of the graphs. Round your result to three decimal places. $$\begin{array}{l}y_{1}=3.25 \\\y_{2}=\frac{1}{2} \ln (x+2)\end{array}$$

Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer(s) using a graphing utility. $$\log _{12} x^{2}=6$$

The percent \(p\) (in decimal form) of the United States population who own a smartphone is given by $$p=\frac{1}{1+e^{-(t-93) / 22.5}}$$ where \(t\) is the number of months after smartphones were available on the market. Find the number of months \(t\) when the percent of the population owning smartphones is (a) \(50 \%\) and (b) \(80 \%\).

Find the time required for a \(\$ 1000\) investment to (a) double at interest rate \(r,\) compounded continuously, and (b) triple at interest rate \(r\), compounded continuously. Round your results to two decimal places. $$r=7 \%$$

Use the regression feature of a graphing utility to find a power model \(y=a x^{b}\) for the data and identify the coefficient of determination. Use the graphing utility to plot the data and graph the model in the same viewing window. $$(2,450),(4,385),(6,345),(8,332),(10,312)$$
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