Functions can be represented as equations, and equations can be represented as functions.
The number of people that started the rumor is 10
The function is represented as:
[tex]\mathbf{N(t) = \frac{400}{1 + 39e^{-0.7t}}}[/tex]
To calculate the number of people that started the rumor, we simply set t to 0.
So, we have:
[tex]\mathbf{N(0) = \frac{400}{1 + 39e^{-0.7 \times 0}}}[/tex]
Evaluate the exponent of e
[tex]\mathbf{N(0) = \frac{400}{1 + 39e^{0}}}[/tex]
Express e^0 as 1
[tex]\mathbf{N(0) = \frac{400}{1 + 39\times 1}}[/tex]
Multiply 39 and 1
[tex]\mathbf{N(0) = \frac{400}{1 + 39}}[/tex]
Add 1 and 39
[tex]\mathbf{N(0) = \frac{400}{40}}[/tex]
Divide 400 by 40
[tex]\mathbf{N(0) = 10}[/tex]
When t = 0, N(t) = 10
This means that 10 people started the rumor.
Hence, the number of people that started the rumor is 10
Read more about functions and equations at:
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