Lesson 4-2: Logarithms and Exponential Models
** Logs and exponents cancel each other “undo”
Example 1:
In the last unit we solved the function g(x) = 30(1.05)t for g(x) = 48 by graphing.
Now we are going to solve for t using logs.
Example 2:
The US population is growing continuously and represented by the
function P = 263e0.009t, when does the population reach 300 million, use t = 0 in
1995.
Example 3:
A population of town A begins at P = 1000(1.08)t and a population of town
B begins at P = 2500(0.9)t. When will the population of town A be equal to
town B?
Example 4:
Doubling Time: period of time when function doubles between periods.
a. Find the time needed to double the population given P = 175(1.145)t.
b. How long will it take to quadruple in size? 8 times?
Half-Life of a Quantity
Example 5: Carbon-14 decays at a constant rate of 0.0121%. Find the half-life
of Carbon-14.
In _____________ years you will have half the amount you started with.
Independent:
1. A substance decays by the formula Q = Q0e-kt where t is in minutes. If the
half -life is in 11 minutes, what is k? (k is the rate of decay)
Converting between f(x) = abt & f(x) = aekt
Example 6: Convert the function P = 175(1.145)t to P = aekt
Example 7: Convert Q = 7e0.3t to Q = abt
Independent:
2. Convert the function P = 200(.886)t to P = aekt