1. 7.1 – 7.2 Practice

2. Rewrite in the form y = abx
𝑦=2041∙ 49 𝑥

3. Solve the equation
81 3𝑛 −𝑛 = 3 4
X = -4/17

4. Find the domain and range. y = -1 D: all reals, R: y > -1
Fill in the 2 tables.
Find the asymptote.
Find the domain and range.
y = -1
D: all reals, R: y > -1 x y x y

5. Solve the equation
81 𝑥 ∙ 27 𝑥 2 =81
X = -2, 2/3

6. Write an exponential function in the form y = abx for the curve that passes through (6, 8) (7, 32).
𝑦= 𝑥

7. In 1991, there were 25. 2 computers per 100 people
In 1991, there were 25.2 computers per 100 people. From 1991 through 1995, the number of computers C per 100 people worldwide increased 15% each year.
Write an equation to model this growth, where t is the number of years since 1991.
C=25.2(1.15)t
Use this model to estimate the number of computers per 100 people in Does this estimate seem valid?
721 Computers, NO!

8. Solve the equation
16 𝑥 ∙ 64 3−3𝑥 >64
X < 6/7

9. A tool and die business purchases a piece of equipment for $250,000
A tool and die business purchases a piece of equipment for $250,000. The value of the equipment depreciates at a rate of 12% each year.
a) Write an exponential decay model for the value of the equipment.
y = 250,000(.88)t
b) What is the value of the equipment after 5 years?
$131,932.98

10. Rewrite in the form y = abx
𝑦= 𝑥

11. In 1859 in Australia, 25 rabbits were in imported from Europe as a new source of food. Rabbits are not native to Australia, but conditions were ideal, and they flourished. Soon, the population grew beyond control and the government sought a way to control the rabbit population. 25 rabbits are introduced to an area. Assume the population doubles every six months.
a) Write a model for exponential growth of the situation.
y = 25 (2)2t or y = 25 (4)t
b) How many will there be after 10 years?
26, 214,400 rabbits
c) Estimate the year when the population reaches one million rabbits .
8 years

12. Solve the equation
6 −2𝑥 ∙ 6 −𝑥 = 1 216
X = 1

13. Find the domain and range. y = -5 D: all reals, R: y < -5
Fill in the 2 tables
Find the asymptote.
Find the domain and range.
y = -5
D: all reals, R: y < -5 x y x y

14. Ten grams of Carbon 14 is stored in a container
Ten grams of Carbon 14 is stored in a container. The amount C (in grams) of Carbon 14 present after t years can be modeled by C=10(.99987)t.
What is the rate of decay for Carbon 14?
0.013%
How much Carbon 14 is present after 1000 years?
8.78 grams