9  Algebraic Biology

We’re going to do some Algebra problems with a biological bent now:

1. Problem 1: Population Growth (:ANS)
   • Scenario: A bacterial population doubles every 3 hours. If the initial population is 100 bacteria, write the equation for the population growth and find the population after 9 hours.
2. Problem 2: Photosynthesis Efficiency (:ANS)
   • Scenario: In a photosynthesis experiment, a plant absorbs 48 grams of \(CO_2\) and produces \(C_6H_{12}O_6\) and \(O_2\). How many grams of glucose are produced if the process is 100% efficient?
3. Problem 3: Genetic Probability (:ANS)
   • Scenario: In a genetic cross, the probability of inheriting a certain trait is governed by a quadratic equation \(0.25x^2 + 0.5x + 0.25 = 1\). Solve for \(x\).
4. Problem 4: Enzyme Activity (:ANS)
   • Scenario: The activity of an enzyme is modeled by the quadratic function \(A(t) = -2t^2 + 4t + 6\), where \(A\) is the activity level and \(t\) is time in hours. Find the time when enzyme activity is at its maximum.