Question

fiona started her study of bacteria growth with 1,000 bacteria in a petri dish. after 1 hour, the count was increased to 1,800. after 2 hours, the count was 3,240. after the third hour showed a count of 5,832, fiona wrote an equation to represent the exponential growth of the bacteria. what exponential growth function did fiona write? f(x) = dropdown with 0.55, 1.8, 1000, 1800 dropdown ^x

Explanation:

Step1: Recall exponential growth formula

The general form of an exponential growth function is \( f(x) = a \cdot b^x \), where \( a \) is the initial amount, and \( b \) is the growth factor.

Step2: Determine the initial amount \( a \)

Fiona started with 1,000 bacteria. So, the initial amount \( a = 1000 \).

Step3: Determine the growth factor \( b \)

To find \( b \), we can use the fact that after 1 hour (\( x = 1 \)), the number of bacteria is 1800. Substitute \( x = 1 \), \( f(1) = 1800 \), and \( a = 1000 \) into the formula:
\( 1800 = 1000 \cdot b^1 \)
Divide both sides by 1000: \( b=\frac{1800}{1000}=1.8 \)

Step4: Write the exponential function

Substitute \( a = 1000 \) and \( b = 1.8 \) into the general formula: \( f(x)=1000\cdot1.8^x \)

Answer:

The first box should be filled with 1000 and the second box with 1.8, so the function is \( f(x) = 1000(1.8)^x \)