Download Algebra 2 Pre AP PS: Logarithm Word Problems and Solving

Algebra 2 Pre AP
PS: Logarithm Word Problems and Solving Equations
Part 1: Word Problem Fun. Solve the following exponential problems.
1. Jonas purchased a new car for $15,000. Each year the value of the car depreciates by 30% of its value
the previous year. In how many years will the car be worth $500? Write an equation and solve. Round to
hundredths. (9.53 years)
2. Brad created a chart that shows the population of a town will increase to 96,627 people from a current
population of 11,211 people. The rate of increase is an annual increase of 4.18%. Brad forgot to include
the number of years this increase will take. How many years was it? Round to tenths. (52.6 years)
3. Jack planted a mysterious bean just outside his kitchen window. It immediately sprouted 2.56 cm above
the ground. Jack kept a careful record of the plant’s growth. He measured the height of the plant each
day at 8am and recorded these data.
a. Define variables and write an exponential equation for this pattern. If the pattern were to continue,
what would be the height on the fifth day? (250cm)
b. Jack’s younger brother measured the plant at 8pm on the evening of the third day and found it to be
about 63.25 cm tall. What would you need to plug in for x to calculate this value? Check your answer
(3.5)
c. Find the height of the sprout at 12noon on the sixth day. (728.12cm)
d. Find at what time the sprout has doubled in height. (2:09am)
e. Find the day and time when the plant reaches a height of 1 km. (Day 9, 8:02am)
4. Cristo looks at an old radio dial and notices that the numbers are not evenly spaced. He hypothesizes
that there is an exponential relationship involved. He tunes the radio to 88.7FM. After 6 “clicks” of the
tuning knob, he is listening to 92.9FM.
a. Write an exponential model to represent the situation. Let x represent the number of “clicks” past
88.7FM and let y represent the station number.
b. Use the equation you have found to determine how many “clicks” Cristo should turn to get from
88.7FM to 106.3FM. Round to the nearest whole click (24 clicks)
5. Newton’s Law of Cooling describes the way the temperature of objects adjusts to the ambient
temperature over time. This relationship is an exponential function.
Let H(t ) = 93(0.91)t + 68 describe the temperature of a beverage (in degrees F) t minutes after a
Dunkin’ Donuts employee hands it to you.
a. How can you determine from the equation that the liquid is cooling and not getting hotter?
b. At what temperature is Dunkin Donuts keeping their coffee? (151F)
c. What is the coldest temperature that the coffee will reach? (68F)
f. What is the value of H(10) and what meaning does it have in context? Round to hundredths (104.22F)
g. After how many minutes and seconds will the temperature hit 90°? Solve with logs. (15min & 17sec)
h. After how many minutes and seconds will the temperature hit 75°? Solve with logs. (21 min)
Part 2: Solving Equations
So far you have practiced how to solve linear, absolute value, quadratic, square root, polynomial, exponential and
logarithm equations. Each type of equation has its own path to it’s+3=-16v solution. Let’s take a trip down
memory lane…
Solve each equation ALGEBRAICALLY and label the type of equation (linear, absolute value, quadratic…) Check
your answers with a graphing calculator, plugging in the left side of the equation for y1, and the right side for
y2
6.
10  x =12
7.
9. (x-7)(x+2)(x+3)(x-4)=0
3+4(x-2)-10x=18
10. x = 5+
12. log2(x) =-3
13.
Answers for 6-14 Scrambled

2 2
x
x 2
3x  5
 2
8. 5x2 +3=-16x
11. 2x3=8x
14. 3+ 2  4x-2 =17
x=5/4
x= -3, -1/5
x= 10,& 3
x= 1/8
x = -23/6
x=3.40
x= -2, 0, 2
x= -22 , -2
x= 7, -2, -3, 4