Question

Exponential and Logarithm Written AssignmentName__________________1. (5 points each part) Write an exponential equation and use logs to solve.a. The population of rabbits on a rabbit farm increases by 250% each year. Thefarm started its business with 12 rabbits. How long will it take the farm’s rabbitpopulation to grow to 250 rabbits?b. A lab currently has 70 mg of radioactive material that decays at 3.5% per year.Federal regulation for the substance says that the material must be safely storeduntil it reaches its half-life, at which time the material can be disposed. Howmany years will the lab have to safely store the material before disposal?2. (5 points) The size of the population, P, of toads t years after it is introduced in awetlands can be modeled by100011 492tP = + . How long does it take the toadpopulation to reach 750 toads?3. (5 points) Find the hydrogen concentration of tomatoes if its pH is 4.5.(Hint:pH H log += − )

Answer 1

a.

initial population = 12

Apply the formula:

P = p0 e^rt

Where:

P = 250

po= 12

r = growth rate = 250/100 = 2.5

t = time (years)

Replacing:

250 = 12 e^(2.5t)

250/12 = e^(2.5t)

20.84 = e^2 (2.5t)

Apply ln to both sides

ln 20.84 = ln e^2 (2.5t)

ln 20.84= (2.5t) ln e

ln 20.84 = 2.5 t

(ln 20.84)/2.5= t

t = 1.21 years