According to the U.S. Census Bureau, the United States is becoming more diverse. Based on U.S. Census population projections for 2000 to 2050, the projected Hispanic population (in millions) can be modeled by the exponential function h(t) = 37.79(1.021)^t, where t = 0 corresponds to 2000 and 0 ≤ t ≤ 50.

a. Find the projected Hispanic population for 2005. Compare this to the actual value of 42.69 million.

b. The U.S. Asian population is also growing exponentially, and the projected Asian population (in millions) can be modeled by the exponential function a(t) = 11.14(1.023)^t, where t = 0 corresponds to 2000 and 0 ≤ t ≤ 50. Find the projected Asian population for 2005, and compare this to the actual value of 12.69 million.

c. Determine the expected annual percentage increase for Hispanics and for Asians. Which minority population, Hispanic or Asian, is growing at a faster rate?

d. The U.S. black population is growing at a linear rate, and the projected black population (in millions) can be modeled by the linear function b(t) = 0.5116t + 35.43, where t = 0 corresponds to 2000 and 0 ≤ t ≤ 50. Find the projected black population for 2005 and compare this projection to the actual value of 37.91 million.

e. Graph the projected population function for Hispanics and estimate when the Hispanic population will be double its actual value for 2005. Then do the same for the Asian and black populations. Comment on the accuracy of these numbers.