The exact differential equation problem is discussed on page 62. Verify the exactness of the given equation and solve it step-by-step. Clearly show all calculations, including how exactness is determined. Instructions: Focus strictly on the problem. Provide a detailed step-by-step solution and show all calculations clearly. Irrelevant answers will not be accepted. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.

Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.

The third bacteria culture started with 5,000 bacteria. The assistant found that after 3 hours the estimated population was 80,000. 3. How long did it take for the population to double for the first time? How long after that (a) will it take for the population to double the second time? How long after that will it take for the population to double the third time? Find an equation that can be used to predict the size of the population at any time t. Estimate the population after 3.5 hours. (b) (c) How does the doubling time found in (a) relate to your equation in (b)? Find a general formula (or rule) that can be used to predict the bacteria population for any culture. You should define what each variable in your general formula stands for. You should illustrate how your general formula applies to each of the three scenarios in this investigation! 4.