The amount of a certain radioactive material (in grams) in a storage facility at time t is given by C(t)=81 e 19t, where time is measured in years. (a) How much of the radioactive material was present initially? (b) What is the half-life of the radioactive material? (Hint: For what value of t is C(t) = 40.5?) (a) Initially, there were grams of the radioactive material. (Round to two decimal places as needed.) (...)

The population of Nevada was 3.0 million in 2018 and 2.7 million in 2010. Assuming an exponential model: (a) Write the population of Nevada in the form N= Noat, where N is the population of Nevada in millions, No and a are constants, and t is time in years since 2010. NOTE: Enter the exact answer for No. Enter an exact value for a or round to 4 decimal places. N (t): - (b) What was the estimated population of Nevada in 1996? NOTE: Round your answer to 3 decimal places. The population in 1996 was approximately million people.

4. Exponential Calculation A. The amount of algae in the petri dish of a mad scientist changes based on the following rules: (a) The amount of algae is modeled by exponential growth or decay depending on the time, starting with 3.1 grams. 0.1 (b) Every 2 days, the rate of change of the algae changes,, alternating between two modes: a(t+1) = 0.1a(n) where n is the day the change, and a(+1) a(t) Starting with the first. = = B. Find the amount after 7 days. 5. Suppose f(n) = xn is a function defined for all integers greater than 1 such that: I log2 In +log3 n... logn n = 1 for all integers n > 1. log₂ 2 = 1 A. Find the value of f(2)= x2 that solves:

18 The half-life of a radioactive element can be modelled by M M where M, is the initial mass of the element, t is the elapsed time in hours, and M is the mass that remains after time t. The half-life of the element is