Question

The number of pollinated flowers as a function of time in days can be represented by the function.

f(x)=(3)^(x/2)
What is the average increase in the number of flowers pollinated per day between days 4 and 10?
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Answer 1

So in this case f(x) is number of pollinated flowers and x is the days. First you will need to determine the number of flowers pollinated at days 4 and 10 and the days in between. f(4)= 3(4^2)= 3*16 = 48 f(5)= 3(5^2)= 3*25 =75 f(6)= 3(6^2)=3*36=108 f(7)= 3(7^2)=3*49=147 f(8)= 3(8^2)=3*64=192 f(9)= 3(9^2)= 3*81=243 f(10)= 3(10^2)=3*100=300 Now we need to find the average increase, so that will be the average of the differences between days [(75-48)+(108-75)+(147-108)+(192-147)+(243-192)+(300-243)]/6 =(27+33+39+45+51+57)/6=42

Answer 2

The average increase in the number of flowers pollinated per day between days 4 and 10 is approximately 39 flowers.

Step-by-step explanation:

To find the average increase in pollinated flowers, we need to calculate the difference in the number of flowers between days 4 and 10 and then divide by the number of days (6). Here's how we can do it:

Calculate the number of flowers pollinated on days 4 and 10:

f(4) = (3)^(4/2) ≈ 18.4 flowers

f(10) = (3)^(10/2) ≈ 57.4 flowers

Calculate the increase in flowers:

Increase = f(10) - f(4) ≈ 57.4 flowers - 18.4 flowers ≈ 39 flowers

Calculate the average increase per day:

Average increase = Increase / Number of days

Average increase ≈ 39 flowers / 6 days ≈ 6.5 flowers/day

Therefore, the average increase in the number of flowers pollinated per day between days 4 and 10 is approximately 6.5 flowers, or 39 flowers in total.

Note: The function f(x) = (3)^(x/2) is an exponential function, which means the number of pollinated flowers increases rapidly as the days go by. This explains why the average increase per day is quite high between days 4 and 10, even though it's just a six-day period.