[size=150]The equation [math]p\left(h\right)=5,000\cdot2^h[/math] represents a bacteria population as a function of time in hours. Here is a graph of the function [math]p[/math].[/size][br][img]data:image/png;base64,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[/img][br][br]Use the graph to determine when the population will reach 100,000.
Explain why [math]\log_220[/math] also tells us when the population will reach 100,000.[br]
[size=150]Population growth in the U.S. between 1800 and 1850, in millions, can be represented by the function [math]f[/math], defined by [math]f\left(t\right)=5\cdot e^{\left(0.028t\right)}[/math].[/size][br][br]What was the U.S. population in 1800?[br]
Use graphing technology below to graph the equations [math]y=f\left(t\right)[/math] and [math]y=20[/math]. Adjust the graphing window to the following boundaries: [math]0<[/math][math]x[/math][math]<100[/math] and [math]0<[/math][math]y[/math][math]<40[/math].
What is the point of intersection of the two graphs, and what does it mean in this situation?[br]
[math]\log_b\frac{1}{9}=\text{-}2[/math]
[size=150]Solve [math]9\cdot10^{\left(0.2t\right)}=900[/math]. [/size]Show your reasoning.
Explain why [math]\ln4[/math] is greater than 1 but is less than 2.