Question

suppose the function f(t) = e^t describes the growth of a colony of bacteria, where t is hours. find the number of bacteria present at 5 hours.
a) 79.432
b) 148.413
c) 59.598
d) 8.155
question 6 (5 points)
does the function f(x) = 2e^(-x) represent exponential growth, decay, or neither?
a) exponential decay
b) impossible to determine with the information given.
c) neither

Explanation:

Step1: Substitute t value

We are given the function $f(t)=e^{t}$ and we need to find the value when $t = 5$. So we substitute $t=5$ into the function: $f(5)=e^{5}$.

Step2: Calculate the result

Using a calculator, $e^{5}\approx148.413$.

For the second - part:

Step1: Recall exponential form

The general form of an exponential function is $y = a\cdot e^{kx}$, where $a
eq0$, $k$ is a real number. If $k>0$, it is exponential growth; if $k < 0$, it is exponential decay.
For the function $f(x)=2e^{-x}=2\cdot e^{(- 1)x}$, here $k=-1<0$.

Answer:

B. 148.413