91Ó°ÊÓ

Write the exponential functions in the form \(Q=a e^{k t}\) and state the values of \(a\) and \(k\). $$ Q=37.5\left(e^{1-3 t}\right)^{2} $$

What do the functions tell you about the quantities they describe? The size \(P\) of a population of animals in year \(t\) is \(P=1200(0.985)^{12 t}\)

Based on Table 10.9 , which gives values of the exponential function \(Q=12(1.32)^{t}\). Your answers may be approximate. $$ \begin{array}{c|c|c|c|c|c|c} \hline t & 2.0 & 2.2 & 2.4 & 2.6 & 2.8 & 3.0 \\ \hline Q & 20.9 & 22.1 & 23.4 & 24.7 & 26.1 & 27.6 \\ \hline \end{array} $$ $$ \text { Solve } 12(1.032)^{t}=25 $$

Can the quantities be represented by exponential functions? Explain. The speed of personal computers if it doubles every 3 years.

In Exercises \(11-14\) give the growth rate that corresponds to the given growth factor. 1.7

Write the exponential functions in the form \(Q=a e^{k t}\) and state the values of \(a\) and \(k\). $$ Q=\frac{e^{\pi} e^{2 t}}{e^{7 t}} $$

Find the annual growth rate of the quantities described.The value of a house triples over a 14-year period.

Find the annual growth rate of the quantities described. A population goes down by half after 7 years.

Write the exponential functions in the form \(Q=a e^{k t}\) and state the values of \(a\) and \(k\). $$ Q=90 \sqrt{e^{-0.4 t}} $$

Find values for the constants \(a, b,\) and \(T\) so that the quantities described are represented by the \(Q=a b^{t / T}\) A population begins with 1000 members and doubles every twelve years.