Help with exponential function word problem

This is because B(t) represents the number of bacteria, not the number of days. In summary, after 2 days, there will be approximately 132.8 bacteria in the culture according to the given equation.
  • #1
linapril
23
0
The number of bacteria in a culture is given by B(t) = 40e0.6t, where t is the time in days.
How many bacteria are there after 2 days?
I substituted t = 2, and got this:

2B = 40e1.2
which I simplified to become this
B = 66.4 days

Apparently this answer is wrong though, can someone explain why?
 
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  • #2
linapril said:
The number of bacteria in a culture is given by B(t) = 40e0.6t, where t is the time in days.
How many bacteria are there after 2 days?
I substituted t = 2, and got this:

2B = 40e1.2
which I simplified to become this
B = 66.4 days

Apparently this answer is wrong though, can someone explain why?

Hi linapril! :)

After substitution you have B(2) = 40e1.2
The left side B(2) is not a multiplication.
B(2) is a special notation that represents the number of bacteria after 2 days.
We say that B is a function of time.

So your answer is just 40e1.2 = 132.8 days.
 
  • #3
However, the answer is NOT "132.8 days" it is, rather, 132.8 bacteria.
 

FAQ: Help with exponential function word problem

What is an exponential function?

An exponential function is a mathematical function in which the independent variable appears in the exponent. It is commonly written in the form of f(x) = ab^x, where a is the initial value and b is the base.

How do I solve a word problem involving exponential functions?

To solve a word problem involving exponential functions, you first need to identify the given information and formulate an equation using the given values. Then, you can use algebraic techniques such as substitution or logarithms to solve for the unknown variable.

What are some real-life applications of exponential functions?

Exponential functions can be used to model population growth, compound interest, radioactive decay, and other natural phenomena. They are also commonly used in economics, finance, and biology.

How do I graph an exponential function?

To graph an exponential function, you can create a table of values by plugging in different values for the independent variable, and then plot those points on a coordinate plane. Alternatively, you can use the properties of exponential functions to identify key points on the graph.

What is the difference between exponential growth and decay?

Exponential growth occurs when the base of an exponential function is greater than 1, resulting in a continuously increasing graph. Exponential decay, on the other hand, occurs when the base is between 0 and 1, resulting in a continuously decreasing graph.

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