Question

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

Answer 1

This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay.

Answer 2

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

`N(t) = 300\cdot 2^{-(t)/(8)}`
The question is:
Is this exponential growth or decay? Explain using your understanding of the properties of exponents.
This is an exponential decay.
In general, we can write down exponential functions like this:

`f(x)=b^(ax)`
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:

`f(x)=b^(-ax)=(1)/(b^(ax))`
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.