MATH SOLVE

10 months ago

Q:
# the function below represents the number of zombies, N, where t is the number of years since the zombies gained control of earth

Accepted Solution

A:

There is missing information about this question that I found online.

Given function is:

[tex]N(t) = 300\cdot 2^{-\frac{t}{8}}[/tex]

The question is:

Is this exponential growth or decay? Explain using your understanding of the properties of exponents.

This is an exponential decay.Β

In general, we can write down exponential functions like this:

[tex]f(x)=b^{ax}[/tex]

Parameter a is the key parameter that will tell how exponential function behaves. If it is positive we have an exponential growth. If it is negative we can rewrite function like this:

[tex]f(x)=b^{-ax}=\frac{1}{b^{ax}}[/tex]

We can notice that in this case, the denominator will exhibit exponential growth, in other words, the functions rapidly declines. This is an exponential decay.

Given function is:

[tex]N(t) = 300\cdot 2^{-\frac{t}{8}}[/tex]

The question is:

Is this exponential growth or decay? Explain using your understanding of the properties of exponents.

This is an exponential decay.Β

In general, we can write down exponential functions like this:

[tex]f(x)=b^{ax}[/tex]

Parameter a is the key parameter that will tell how exponential function behaves. If it is positive we have an exponential growth. If it is negative we can rewrite function like this:

[tex]f(x)=b^{-ax}=\frac{1}{b^{ax}}[/tex]

We can notice that in this case, the denominator will exhibit exponential growth, in other words, the functions rapidly declines. This is an exponential decay.