Question

a population of bacteria triples every hour. is this situation linear or exponential?
a) exponential, because the function decreases
b) linear, because the function increases by a common difference
c) linear, because the function increases
d) exponential, because the function grows by a common ratio
question 18 (5 points)
identify the recursive formula for the sequence 20, 28, 36, 44, ....
a) $f(n)=\begin{cases}f(1) = 20\\f(n)=f(n - 1)+8 \text{ if }n>1end{cases}$
b) $f(n)=\begin{cases}f(1) = 20\\f(n)=f(n - 1)+8 \text{ if }n>0end{cases}$
c) $f(n)=\begin{cases}f(1) = 20\\f(n)=f(n - 1)-8 \text{ if }n>0end{cases}$

Explanation:

Question 1

Step1: Recall linear and exponential growth

Linear growth has a constant difference, exponential has a constant ratio.

Step2: Analyze bacteria growth

Bacteria triples every hour, ratio of 3.

Step1: Find the common difference

$28 - 20=8$, $36 - 28 = 8$, $44 - 36=8$.

Step2: Determine recursive formula

First - term $f(1)=20$, $f(n)=f(n - 1)+8$ for $n>1$.

Answer:

D. Exponential, because the function grows by a common ratio

Question 2