1. On April 1, 2022 there are 200 cases of a new variant of a virus that was just discovered. On April 5, 2022, 320 total cases have been diagnosed of this variant of a virus.
   1. Assuming an exponential growth model N(t) =N0e kt for the growing number of total cases, find the growth constant k. Round your answer for k to 4 decimal places. Let t be measured in days, where t=0 days represents April 1, 2022.
   2. Find the exponential growth function N(t) which gives the total number of cases after t days. Make sure you plug in all the constants you have for the function, such as N0 and k.
   3. If the total number of cases of this variant virus grows according to this exponential growth model, when will there be 10,000 total cases?
   4. How many total cases does this model predict that there will be on May 1, 2022? (Round your answer to the nearest case.)