7.1 Exploring Exponential Models

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Repeated multiplication can be represented by an exponential function. It has the general form where

***x has D: all real numbers

xaby 1,0,0 bba

Ex 1) Graph xy 2

Ex) Determine if the function represents exponential growth or decay. State the y-intercept and the asymptote.

xy )95.0(12 xy )2(25.0

Note that b=1+r. The value b is called the growth or decay factor. The value r is called the growth or decay rate and is usually a percentage represented by a decimal.

Ex) You invested $1000 in a savings account at the end of the 6th grade. The account pays 5% annual interest. How much money will be in the account after six years?

Ex) Suppose you invest $1000 in a savingsAccount that pays 5% annual interest. If you make no additional deposits or withdrawals, how many years will it take for the account to grow to at least $1500?

To model a discrete situation with anexponential model, you need to find b. If you know y –values for two consecutivex-values, you can find the rate of change using the formula and thenb=1+r. 1

12

y

yyr

Ex) The table shows the world populationof the Iberian lynx in 2003 and 2004. If thistrend continues and the population is decreasing exponentially, how many Iberian lynx will there be in 2014?