A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days: f(n) = 10(1.02)n1. Starting from 0 days, plug x-values into our function to find out how many days it takes for the plant to grow to 11.04 cm2. Write a compound inequality to show the reasonable domain of the plant growth:3. What is the y-intercept of our function? 4. What does the y-intercept of the graph of the function f(n) represent? 5. What is the average rate of change formula for exponential growth functions?6. Plug and chug n= 1 to n = 5 into your formula above. Show all work! 7. What does the average rate of change answer represent?

Answer:Step-by-step explanation:Given that the  height of the plant f(n), in cm, after n days:[tex]f(n) = 10(1.02)^n[/tex]To find n when f(n) = 11.04 cm[tex]11.04 = 10(1.04)^n\\n log 1.04= log 11.04 -log 10\\\\n=\frac{0.04296}{0.0170} \\=2.527[/tex]i.e. in 2.5 days2) n cannot go upto infinityIf maximum growth is h, then domain is (0, [tex]\frac{log h - log 10}{log 1.04}[/tex])3) Put n=0 y intercept = 10 cm.4) This gives the initial height of the plant i.e. when n =05) Average rate of change = 10(1.04)^n ln 1.046) n =1,2,3,4,5n 1      2               3        4                         5 f(n) 10.4 10.816 11.24864 11.6985856 12.16652902 (this is got by substituting n =1,2,3,4,5.7) Avg rate of change in interval (a,b) = change in f(n)/change in n