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)
Stacey Warren - Expert brainly.com
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A. 0 thru 5 (integers) ... (look at part C)
B. the starting height of the plant
C. f(1) = 10.02 .... f(5) = 11.041
m(ave) = (11.041 - 10.02) / (5 - 1) = 0.255 cm/day
this represents the average change of height each day for this time.
Can I get the explanations please?
For the firat part you need toknow what reasonable values of n will be plotted on the chart
you know that at the end of the trial (i.e after n days) the height is
but also that this is 10(1.02)^n
so use logs to find n
ok, im confused
the trial lasts n days
after n days the height is 11.04cm
but height = 10(1.02)^n
so 11.04 = 10 (1.02)^n
use the propoerties of logs and exponents to find n
oh ok, so n = 5?
did oyu use the properties of logs and exponents to get that?
11.04 = 10(1.02)^n
10(1.02)^n = 11.04
10(1.02)^n/10 = 11.04/10
1.02^n = 1.104
log(1.02)^n = log(1.104)
n*(log(1.02)) = log(1.104)
n = log(1.104)/(log(1.02)
n = 4.99 (round to 5)
OK well done
now second part
the y intercept is when n=0
what does that value mean?
It represents the starting population. right?
not the population - since we are measuring height (but I think you've got the right idea)
(this exponential function of DOES represent populations! :-)
Ok so that's part b?
so wht IS the staring height (it doesnt ask oyu that - but you maybe would lik eot know?)
Um... .21 cm?
put n= 0 into the equation for height....
Ok... But the answer cant be true...
You should also get into th ehabit of doing a 'sanity check' on oyur answers
If it is 11cm after 5 days it cannot be 21cm at start.
And the answer CAN be true
what is 1.02^0??
so 10* (1.02)^0 is??
Im srry, I thought you meant to do the whole equation with 11.04=10(1.02)^0
so it starts at 10cm
and grows to 11.04 in 5 days
the 3rd part says
find change of height over 4 days and divide by 4 days
so what does that give you?