Math Reflection: Investigation 1
1) Describe and exponential growth factor. Include key properties such as growth factors.
An exponential growth pattern is something that grows at a constant amount. The previous amount is multiplied by a growth factor.
Example: Growth factor of 2, or doubling.
1, 2, 4, 8, 16, 32, 62, 128, 512, 1024, 2048, 4096...
2) How are exponential functions similar to and different from the linear functions you worked with in earlier units?
Exponential functions are similar to linear functions because both have y-intercepts. They can both be graphed, have and equation, and table. Exponential functions are different than linear functions because exponential functions have growth factors, but linear functions have slopes. Linear functions go up by a constant rate of change, but exponential functions don't. The graph for linear functions include straight lines whereas the ones for exponential functions are curved. Linear equations take the form of y=mx+b, but exponential functions take the form of y=a(b)^x.
Example:
Exponential: y=6(0.8)^x
Linear: y=0.8x+6
These both result in different tables and graphs, but they both will start at the same initial amount.
An exponential growth pattern is something that grows at a constant amount. The previous amount is multiplied by a growth factor.
Example: Growth factor of 2, or doubling.
1, 2, 4, 8, 16, 32, 62, 128, 512, 1024, 2048, 4096...
2) How are exponential functions similar to and different from the linear functions you worked with in earlier units?
Exponential functions are similar to linear functions because both have y-intercepts. They can both be graphed, have and equation, and table. Exponential functions are different than linear functions because exponential functions have growth factors, but linear functions have slopes. Linear functions go up by a constant rate of change, but exponential functions don't. The graph for linear functions include straight lines whereas the ones for exponential functions are curved. Linear equations take the form of y=mx+b, but exponential functions take the form of y=a(b)^x.
Example:
Exponential: y=6(0.8)^x
Linear: y=0.8x+6
These both result in different tables and graphs, but they both will start at the same initial amount.
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