y = abx is the general form of an exponential equation and what determines growth or decay is the b value. The a value is not there, so it is 1. That means the b value must be 3.
Answer
Exponential growth.
Example 3
Is f(x) exponential growth or decay? f(x) = 2(0.1)10x
Hint
y = abx is the general form of an exponential equation and what determines growth or decay is the b value. The b value is 0.1.
Answer
Exponential decay.
Example 4
The population of Shmooptown is defined by the function P(t) = 760,000(1.0145)t. What will the population be in 10 years?
Hint
Substitute a 10 for the t variable in the Shmooptown population equation.
Answer
Around 877676.
Example 5
Determine the exponential function if the initial value is 12 and it is increasing a rate of 50% each year.
Hint
y = abx is the general form of an exponential equation. Substitute the 12 as the initial value and don't forget to set b = (1 + 0.5).
Answer
y = 12(1.5)x
Example 6
What is the exponential function based on this table of values?
Hint
f(0) = 10000. Find out how much you are multiplying each y value by to get the b value.
