Madison is organizing her bookshelf. She places her favorite book on the first shelf. She puts 2 books on the second shelf and 4 books on the third shelf. She continues by putting 8 books on the fourth shelf and 16 books on the fifth shelf. She has one more shelf left. Answer the following:
If this pattern continues, how many books will be on the last shelf? In a complete sentence, explain how you found your answer.

Drag the tiles to the correct boxes to complete the pairs. label each function. as even , odd, or neither.

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?

Apply the distributive property to simplify the expression. −4(5x + 2)