Final answer:
The number of employees needed based on the temperature t is expressed as e(t) = -0.02t^2 + 0.88t + 3, derived by substituting the visitor formula into the employee estimate formula.
Step-by-step explanation:
To express the number of employees needed e(t) in terms of the temperature t, we first need to use the zoo's prediction of visitors v(t) given by v(t) = 88t - 2t2. Then, the formula to estimate the number of employees needed based on the number of visitors x is e(x) = 0.01x + 3. Therefore, we substitute the expression for v(t) into the formula for e(x) to find e(t) in terms of t.
Step 1: Substitute v(t) into e(x):
e(t) = 0.01(88t - 2t2) + 3
Step 2: Distribute and simplify:
e(t) = 0.01*88t - 0.01*2t2 + 3
e(t) = 0.88t - 0.02t2 + 3
Therefore, the number of employees needed based on the temperature t is given by e(t) = -0.02t2 + 0.88t + 3.