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. Pick two data points predicted by he research model a(t) to construct a new exponential model b(t) for the number of cumulative AIDS cases. Using a graphing device, sketch a(t) and b(t) simultaneously; discuss how the two models differ and explain the use of the word "relief".