Question

a study is done on the number of bacteria cells in a petri dish. suppose that the population size p(t) after t hours is given by the following exponential function p(t)=1700(1.05)^t. find the initial population size. does the function represent growth or decay? growth decay by what percent does the population size change each hour? %

Explanation:

Step1: Identify initial population

The initial population is the value of $P(t)$ when $t=0$. For $P(t)=1700(1.05)^t$, substitute $t=0$:
$P(0)=1700(1.05)^0 = 1700 \times 1 = 1700$

Step2: Classify growth/decay

Compare the base of the exponent to 1. Since $1.05 > 1$, the function represents growth.

Step3: Calculate hourly percent change

The growth rate is the base minus 1, converted to a percentage:
$(1.05 - 1) \times 100\% = 0.05 \times 100\% = 5\%$

Answer:

Initial population size: 1700
Growth/decay: growth
Hourly percent change: 5%