91Ó°ÊÓ

Write the number in scientific notation. 0.006

The apparent magnitude of a star is a measure of the brightness of the star as it appears to observers on Earth. The apparent magnitude \(M\) of the dimmest star that can be seen with a telescope is \(M=5 \log D+2\), where \(D\) is the diameter (in millimeters) of the telescope's objective lens. What is the diameter of the objective lens of a telescope that can reveal stars with a magnitude of \(12 ?\)

Use the given information to find the amount \(A\) in the account earning compound interest after 6 years when the principal is \(\$ 3500\).\(r=1.26 \%\), compounded monthly

Under certain conditions, the wind speed \(s\) (in knots) at an altitude of \(h\) meters above a grassy plain can be modeled by the function $$ s(h)=2 \ln 100 h . $$ a. By what amount does the wind speed increase when the altitude doubles? b. Show that the given function can be written in terms of common logarithms as $$ s(h)=\frac{2}{\log e}(\log h+2) . $$

Write the number in scientific notation. 5000

Approximate the solution of each equation using the graph. a. \(1-5^{5-x}=-9\) b. \(\log _2 5 x=2\)

Describe the transformation of the graph of \(f\) represented by the graph of \(g\). Then give an equation of the asymptote. \(f(x)=e^x, g(x)=e^x+4\)

Identify the focus, directrix, and axis of symmetry of the parabola. Then graph the equation. \(y=4 x^2\)

Find the inverse of the function. \(y=\log _2 x\)

Write the number in scientific notation. 26,000,000