Molybdenum is a metal that is often used to make alloys. For example, molybdenum is used to make steel alloys in order to increase strength, hardness, conductivity, and resistance to corrosion and wear.

Suppose molybdenum production is modeled using a Gaussian model. For this problem, report your numerical answers rounded to 1 place after the decimal.

(a) Describe how using a Gaussian function to model materials production is different than using an exponential function (feel free to draw pictures to explain). What does the Gaussian function take into account that the exponential function doesn't?

(b) The US molybdenum reserves are estimated to be 5.4 x 106 tonnes, which is 27% of the total global reserves. In 2014, the peak global production occurred at 300,000 tonnes/yr. Calculate the global molybdenum production 53 years after the peak global production.

(c) Microbiologists have found that Ascomycota fungle phylum, a type of fungi, grows in the molybdenum mine outside of Empire, Colorado in the Rockies. Suppose the population of that fungi in the Empire mine is 2 million spores in the year that molybdenum hits its global peak production and in this year the fungi grew at an exponential rate of 1%. Lets suppose that the carrying capacity for that mine is 9.8 million spores and also that the fungi population will reach 4.9 million spores in 2025. Assuming the population of this fungi can be modeled using logistic growth, what is the fungi population in the Empire mine 53 years after the peak global production of molybdenum occurs?