Initially, a population is 500, and it grows by 2% each year. Explain why the population is an exponential function of time.

Find a formula for the population at any time. (Let t represent time in years and P represent the population size.)

Determine the population size after 5 years. (Round your answer to the nearest whole number.)

Which fact from the tinker v. des moines court decision best supports the reasoning that the conduct of the student protesters was protected by the fourteenth amendment, which prohibits deprivation of life, liberty, or property? o a. the record shows that students in some of the schools wore buttons relating to national political campaigns, and some even wore the iron cross, traditionally a symbol of nazism. o b. on the other hand, the court has repeatedly emphasized the need for affirming the comprehensive authority of the states and of school officials, consistent with fundamental constitutional safeguards, to prescribe and control conduct in the schools. c. the action of the school authorities appears to have been based on an urgent wish to avoid the controversy which might result from the expression, even by the silent symbol of armbands, of opposition to this nation's part in the conflagration in vietnam. d. that they are educating the young for citizenship is reason for scrupulous protection of constitutional freedoms of the individual. if we are not to strangle the free mind at its source and teach youth to discount important principles of our government as mere platitudes.