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Module 23

Exponential Functions & Exponential Growth & Decay Functions

Exponential Function A function of the form f(x)=b^x b>0, b is not 1 & x is a real number
Solve for x 2^x=16 <p>2^x=16</p> <p>2^4=16</p> <p>x=4</p>
Solve for x 3^x=9 <p>3^x=9</p> <p>3^2=9</p> <p>x=2</p>
Solve for x 10000^x=100000 <p>10000^x=100000</p> <p>(10^4)^x=10^5</p> <p>10^4x=10^5</p> <p>4x=5</p> <p>x=5/4</p>
One type of uranium has a daily radioactive decay of 0.5%. If 10 pounds of uranium is available today, how much will remain after 10 days. Use y=10(2.7)^-0.005t let t be 10 days <p>y=10(2.7)^-0.005(10)</p> <p>y=10(2.7)^-0.05</p> <p>y=10(0.95155)</p> <p>y~9.55 lbs</p>
Exponential Growth y=C(1+r)^x where C is the initial amount, x is the time interval, r is the growth rate (often %) and (1+r) is growth factor
Find the exponential growth Original amount is $300 Growth rate is 5% Number of years is 8 <p>y=C(1+r)^x</p> <p>y=300(1+0.05)^8</p> <p>y=300(1.48)</p> <p>y~444</p>
Exponential Decay y=C(1-r)^x Where C is the initial amount, r is the decay rate (often %), x is the number of time intervals, (1-r) is decay factor
Created by: dvf2bu