7 7 practice geometric sequences as exponential functions answers


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7-7 Practice Geometric Sequences as Exponential Functions Determine whether each sequence is arithmetic geometric or neither Explain 1 1 –5 –11 –17 

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Review – Sequences Exponential Functions Use inductive reasoning to Find the common ratio of the geometric sequence and then find the next two numbers in 

  • How can you use geometric sequences to define exponential functions?

    Geometric sequences can be modeled by exponential functions using the common ratio and the initial term.
    Exponential growth and exponential decay functions can be used to model situations where a quantity increases or decreases by the same rate in each time period.

  • Is a geometric sequence linear or exponential?

    Geometric sequences (with common ratio not equal to −1, 1 or 0) show exponential growth or exponential decay, as opposed to the linear growth (or decline) of an arithmetic progression such as 4, 15, 26, 37, 48, … (with common difference 11).

  • For linear equations, we have y = m (slope) x + b (y intercept) and for exponential equations we have y = a (initial value)*r(ratio or base)^x.

  • What is the formula for geometric sequence with exponents?

    General Term
    A geometric sequence is an exponential function.
    Instead of y=ax, we write an=crn where r is the common ratio and c is a constant (not the first term of the sequence, however).
    A recursive definition, since each term is found by multiplying the previous term by the common ratio, ak+1=ak * r.

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