The average increase in the number of flowers pollinated per day between days 4 and 10 is <u>39</u>, given that the number of pollinated flowers as a function of time in days can be represented by the function $f(x) = (3)^{\frac{x}{2} }$ .

In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function $f(x) = (3)^{\frac{x}{2} }$ .

To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.

First, we find the value of the function $f(x) = (3)^{\frac{x}{2} }$ , for f(10) and f(4).

$f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243$

$f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9$

Thus, the average increase

= {f(10) - f(4)}/{10 - 4},

= (243 - 9)/(10 - 4),

= 234/6

= 39.

Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is <u>39</u>, given that the number of pollinated flowers as a function of time in days can be represented by the function $f(x) = (3)^{\frac{x}{2} }$ .

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