Question

The number of acres of wetland infested by an invasive plant species after t Years is given by u(t)=12•2^t/3. Solve the equation u(t)=50. What does your answer tell you about the wetland?

Answer 1

For this case we have the following equation:
 u (t) = 12 • 2 ^ t / 3
 We equate the equation for u (t) = 50.
 We have then:
 12 • 2 ^ t / 3 = 50
 We clear the value of t:
 2 ^ t / 3 = 50/12
 log2 (2 ^ t / 3) = log2 (50/12)
 t / 3 = log2 (50/12)
 t = 3 * log2 (50/12)
 t = 6.2 years
 Answer:
 After 6.2 years 50 acres of wetland are infested by an invasive plant species