Question

food poisoning occurs when bacteria like salmonella and listeria grow on food. these microorganisms grow at an exponential rate. when an initial population of 100 bacteria are left at 98 °f, they will grow at a rate of $b = 100(9)^h$. which graph could be used to calculate the number of bacteria after a certain number of hours? graph with b (bacteria) on y - axis (ranging from 500 to 5000) and h (hours) on x - axis, showing an exponential curve starting around (0,1000) and increasing rapidly

Explanation:

Step1: Analyze the function type

The function for the number of bacteria is \( b = 100(8)^h \), which is an exponential growth function. Exponential growth functions have the form \( y = a(b)^x \) where \( a>0 \) and \( b > 1 \), and their graphs are increasing curves that get steeper over time.

Step2: Check the initial condition

When \( h = 0 \) (initial time), \( b=100(8)^0=100\times1 = 100 \). Wait, but the graph shown has a y - intercept around 1000? Wait, maybe there is a typo in the function (maybe \( b = 1000(8)^h \) or the initial value is 1000). Assuming the graph has a y - intercept (when \( h = 0 \)) around 1000 and is an exponential growth curve (increasing, concave up), the given graph (the one with the blue curve starting around 1000 and increasing rapidly) is an exponential growth graph, which matches the behavior of the bacteria growth function (since exponential growth functions have graphs that are increasing and get steeper as \( h \) increases). So the graph shown (the one with the blue curve) is the correct graph for calculating the number of bacteria after a certain number of hours.

Answer:

The graph with the blue curve (the one provided in the image) is the graph that could be used to calculate the number of bacteria after a certain number of hours.