Consider the exponential function f(x) = 2(3x) and its graph.
The initial value of the function is.
The base of the function is.
The function shows exponential
answer
2
3
growth
question
Consider the function f(x) = (6)x. What is the value of the growth factor of the function?
answer
6
question
Which is a stretch of an exponential decay function?
answer
C
question
Which point is on the graph of the function
f(x) = (2)x?
answer
D
question
Consider the table representing an exponential function.
The equation for this function is
f(x) = ()x.
answer
8
0.5
question
Which statements are true about the graph? Check all that apply.
answer
1 4
question
Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.
answer
In the function f(x) = a(b^x), the initial value is always a. This is because a is independent on x. So, when x changes, b^x will change as well but a will remain the same. For example, let a = 2, b = 3, and x = 0: f(0) = 2 * 3^0 = 2 * 1. If x = 1, then f(1) = 2 * 3^1 = 2 * 3. If x = 2, then f(2) = 2 * 3^2 = 2 * 9, etc. As you can notice a = 2 remain unchanged as the initial value, because a is independent on x change.
question
Fiona started her study of bacteria growth with 1,000 bacteria in a petri dish. After 1 hour, the count was increased to 1,800. After 2 hours, the count was 3,240. After the third hour showed a count of 5,832, Fiona wrote an equation to represent the exponential growth of the bacteria. What exponential growth function did Fiona write?
f(x) =
answer
1000
1.8
question
Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number.
There were
1.4
⇒ 59 bacteria after 5 hours.
answer
59
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