91Ó°ÊÓ

A mill in a town with a population of 400 closes and people begin to move away. Find a possible formula for the number of people \(P\) in year \(t\) if each year one-fifth of the remaining population leaves.

Without solving them, say whether the equations in Problem had a positive solution, a negative solution, a zero solution, or no solution. Give a reason for your answer. \(7+2^{y}=5\)

For the functions in the form \(P=a b^{t / T}\) describing population growth. (a) Give the values of the constants \(a, b\), and \(T\). What do these constants tell you about population growth? (b) Give the annual growth rate. \(P=80 \cdot 3^{t / 5}\)

For the functions in the form \(P=a b^{t / T}\) describing population growth. (a) Give the values of the constants \(a, b\), and \(T\). What do these constants tell you about population growth? (b) Give the annual growth rate. \(P=75 \cdot 10^{t / 30}\)

The balance in a bank account grows by a factor of each year and doubles every 7 years. (a) By what factor does the balance change in 1. years? In 21 years? (b) Find \(a\).

Write the exponential functions in the form \(Q=a b^{t},\) and identify the initial value and the growth factor. $$ Q=\frac{50}{2^{t / 12}} $$

Without solving them, say whether the equations in Problem had a positive solution, a negative solution, a zero solution, or no solution. Give a reason for your answer. \(25 \cdot 3^{z}=15\)

Write the exponential functions in the form \(Q=a b^{t},\) and identify the initial value and the growth factor. $$ Q=250 \cdot 5^{-2 t-1} $$

After \(t\) years, an initial population \(P_{0}\) has grown to \(P_{0}(1+r)^{t} .\) If the population at least doubles during the first year, which of the following are possible values of \(r\) ? (a) \(r=2 \%\) (b) \(r=50 \%\) (c) \(r=100 \%\) (d) \(r=200 \%\)

For the functions in the form \(P=a b^{t / T}\) describing population growth. (a) Give the values of the constants \(a, b\), and \(T\). What do these constants tell you about population growth? (b) Give the annual growth rate. \(P=50\left(\frac{1}{2}\right)^{t / 6}\)