1. what is the rule for the base and exponents when multiplying like powers?

2.what must be true about the base of all exponential decay functions?

3.write 216^2/3 in the radical form first and then evaluate. (you must use a calculator, but show your work steps in evaluating to demonstrate your understanding of the root and/or power involved.)

4.the spring break approaching and Mr. White's to-do list for home renovations is growing exponentially. if there are 20 items on his list on the 26th of march, and the number of items grows by 25% per day, how many items will he have on his list by April 9th? round to nearest whole item.

5.A biologist measures 1000 yeast cells in a sample at 12:00 noon. she predicts that under current conditions the number of cells should double every 30 minutes.

a) create an exponential growth model for this situation.

b) how many cells will there be in the sample at 2:30?

6.A hospital uses cobalt-60, which has a half-life of 150 days, for radiotherapy treatment for its cancer patients. The hospital currently has a 70g supply of cobalt-60, and it requires at least 55g for the therapy machine to provide an effective amount of radiation.

a)create an exponential decay model for this situation.

b)how often must the cobalt in the machine be replenished?

7.the number of franchises of a dance studio has been growing exponentially since the first studio opened in 1998. since then the number of studios has grown at a rate of 14% each year.

a) create an algebraic model that gives the number of studios t years after 1998.

b)use your model to predict the number of studios in 2022. round our answer to the nearest whole number.

8.sketch a graph of each of the following exponential functions and complete the table.

a) f(x) = 2^x - 3 b) g(x)= (1/3)^x

Table:

function | y-intercept | equation of the asymptote | domain | range |

f(x)= 2^x - 3 | | | | |

| | | | |

g(x)= (1/3)^x | | | | |

9.a magical lily pad in a lake is growing at an exponential rate and doubles in size every day. after growing for 48 days the lily pad covers the entire lake. on what day did the lily pad cover half of the lake?