Mathematics
GoldenTreptow
2015-11-02 06:25:36
WILL GIVE BRAINLIEST 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)n Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function? (4 points) Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points) Part C: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent? (4 points)
ANSWERS
Maria222
2015-11-02 08:15:17

f(n)=10(1.02)^n f(n)=a1(r)^n a1=10, initial value r=1.02, or 2% increase  Part A.)  (9.5,11.5) would be reasonable as the initial point is 10 and the final point is 11.04. You could also begin at 10 and end at 11.1, if wanting to maximize space used. Part B.) Y-intercept, here being 10, represents the starting point, or initial value, of the height of the plant.  Part C.) ARC: (f(5)-f(1))/(5-1) f(5)=11.04080803 f(1)=10.2 (11.04080803-10.2)/(5-1) (0.84080832)/(4)=0.210202008 cm/n, growth of 0.210202008 cm per n day of growth

ConnieTufte680
2015-11-02 08:16:32

A)[latex]11.04 = 10(1.02)^n 1.104 = 1.02^n [/latex] [latex]1.104 = 1.02^n~ 1.104 = 1.02 n = 1.104/ ln 1.02 n = 4.99630409516 [/latex] 4.99 when rounded B.  [latex]f(0) = 10(1.02)^0 f(0) = 10(1) f(0) = 10 [/latex] C.[latex]f(1) = 10(1.02)^1 f(1) = 10(1.02) f(1) = 10.2 (1, 10.2) f(5) = 10(1.02)^5 f(5) = 10(1.1040808) f(5) = 11.040808 (5, 11.040808) [/latex]

ADD ANSWER