In 1989, research scientists published a model for predicting the cumulative number of AIDS cases reported in the United States: a(t) = 155((t-1980)/10)3, (thousands) where t is the year. This paper was considered a "relief," since there was a fear the correct model would be of exponential type. Use the two data points predicted by the research model a(t) for the years 1985 and 1995 to construct a new exponential model b(t) for the number of cumulative AIDS cases. (Round values to three decimal places.) Discuss how the two models differ and explain the use of the word "relief."

Suppose you know that the mass of a bacteria culture grows exponentially. Using log plots, decide which of the following best estimates the data in this chart. Hour 3 7 Ln(Bacteria Mass) 7.154 7.535 а) BacteriaMass(t) = 961e0.0951 o b) BacteriaMass(t) = 1.1e6.868t %3D с) BacteriaMass(t) = 961t + 0.095 d) BacteriaMass(t) = 1001e0.095t e) BacteriaMass(t) = = 1001e-0.357t

A researcher is studying the effect of parents' level of education on educational achievement of individuals. Using data on completed years of education (educ), mother's level of education (motheduc), father's level of education (fatheduc), a measure of cognitive ability (abil), and logarithm of family income (l.income), the researcher estimates 4 models. Table (1) shows the OLS estimates for each model, with standard errors in parentheses underneath each coefficient. The dependent variable in all the models is educ. Model 1 Model 2 Model 3 Model 4 Independent variables L.income (0.2) 0.15 motheduc 0.27 0.18 0.17 (0.02) (0.03) 0.11 (0.02) 0.52 (0.03) 0.11 (0.02) 0.39 (0.03) 0.10 (0.02) 0.35 fatheduc abil 0.53 (0.03) 0.09 (0.01) 8.74 (0.03) (0.03) (0.03) 0.05 abil_squared ww (0.01) 8.74 6.94 (0.32) 1230 Intercept 8.4 (0.12) 1230 3899.97 0.38 Table (1) (0.31) 1230 (0.31) 1210 N SSR R-squared 3999.24 3785.24 3541.2 0.35 0.45 0.49 a. How the degrees of freedom in model (3) compare to the…

Suppose a study is completed that finds that the number of cockroaches in Chandler decreases by 18% every 12 years. In 2020, there were approximately 3.5 million cockroaches in Chandler. Assuming the number of cockroaches is changing exponentially, how many cockroaches do you estimate there will be in 2025 (5 years later)? Demonstrate mathematically why it is not true that the number of cockroaches in Chandler decreases by 9% every 6 years. Determine how long it will take for the number of cockroaches in Chandler to decrease by 50%.