7.1 – 7.2 Practice.

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7.1 – 7.2 Practice

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

Solve the equation 81 3𝑛+2 243 −𝑛 = 3 4 X = -4/17

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

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

Write an exponential function in the form y = abx for the curve that passes through (6, 8) (7, 32). 𝑦= 1 512 4 𝑥

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 2015. Does this estimate seem valid? 721 Computers, NO!

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

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

Rewrite in the form y = abx 𝑦= 5 3 1 2 𝑥

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

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

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

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