Algebra 1: Unit 8 Geometric Sequences and Exponential Functions

A sequence is defined by $$f\left(1\right)=24$$ and $$f\left(n\right)=\frac{1}{2}f\left(n-1\right)$$ for each whole number n, where $$n>1$$ . What is the 4th term of the sequence?

A sequence can be generated by using $$a_n=4a_{\left(n-1\right)}$$ , where $$a_1=6$$ and n is a whole number greater than 1. What is the 3rd term in the sequence?

A bacteria sample is growing exponentially, as seen in the table below. Which exponential regression equation best represents this data? Round values to the nearest TENTH)

A customer purchases an electronic device for $725. Each year the value of the electronic device decreases by 25%.

Which statement is true about the graph that represents the relationship between the value of the device in dollars, y,  and the number of years, x,  since the device was purchased?

What is the equation of the asymptote of the graph of the function $$y=18\left(0.55\right)^x$$ ?

Move the correct answer to each box. Not all answers will be used.

​ (a)   =​ (b)  

This year the number of students who participated in sports was 418.

Each year the number of students who participate in sports increases by 7%.

What function can be used to model the number of students participating in sports after x  years?

An engineering major at Texas A&M graduates and gets a job working for Texas Instruments. Her starting salary is $75,000 and she has been promised a 9.5% raise each year.

Write a function that models this situation.

Choose the correct answer from each drop-down box to complete the function.

$$f\left(x\right)=$$ ​ (a)   (​ (b)   )^x

The function $$g\left(x\right)=47\left(0.87\right)^x$$ represents the population, in thousands of people, of Wichita, Kansas, where x represents the number of years since 2005.

Choose the correct answer from each drop-down box to complete the statement.

The population of Wichita, Kansas in 2005 was ​ (a)  

The population is ​ (b)   at a rate of ​ (c)   each year.

Which statement about 

$$p\left(x\right)=-8\left(5\right)^x$$

 is true?