91Ó°ÊÓ

Suppose a savings account pays \(5 \%\) interest per year, compounded four times per year. If the savings account starts with \(\$ 600, how many years would it take for the savings account to exceed \)\$ 1400 ?

Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{2}\left(u^{100}\right) $$

Puppose \(r\) is a small positive number. Estimate the slope of the line containing the points \(\left(7, e^{7}\right)\) and \(\left(7+r, e^{7+r}\right)\)

Find all numbers \(x\) that satisfy the given equation.\(e^{x}+e^{-x}=8\)

Find a number \(t\) such that \(\log _{2} t=8\).

Suppose \(r\) is a small positive number. Estimate the slope of the line containing the points \(\left(e^{2}, 6\right)\) and \(\left(e^{2+r}, 6+r\right)\)

Find all numbers \(x\) that satisfy the given equation. \(\log _{7}(x+5)-\log _{7}(x-1)=2\)

Suppose a bank wants to advertise that \(\$ 1000 deposited in its savings account will grow to \)\$ 1040 in one year. This bank compounds interest 12 times per year. What annual interest rate must the bank pay?

Find a number \(y\) such that \(\log _{2} y=-5\).

Suppose a colony of 100 bacteria cells has a continuous growth rate of \(30 \%\) per hour. Suppose a second colony of 200 bacteria cells has a continuous growth rate of \(20 \%\) per hour. How long does it take for the two colonies to have the same number of bacteria cells?