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題目

解題步驟

1. Understand the question

   in a lab experiment, 1,100 bacteria are placed in a petri dish. the conditions are such that the number of bacteria is able to double every 8 hours. write a function showing the number of bacteria after $t$ hours, where the hourly growth rate can be found from a constant in the function. round all coefficients in the function to four decimal places. also, determine the percentage of growth per hour, to the nearest hundredth of a percent.
   answer
   function: $f(t) = \\square(\\square)^\\square$
   growth $\\square$ % increase per hour

2. Explanation

   Step1: Identify initial bacteria count

   The initial number of bacteria $P_0 = 1100$.

   Step2: Find hourly growth factor

   Since bacteria double every 8 hours, solve for growth factor $b$:
   $$2 = b^8 \implies b = 2^{\frac{1}{8}}$$
   Calculate $2^{\frac{1}{8}} \approx 1.0905$.

   Step3: Write exponential growth function

   Use the form $f(t) = P_0 b^t$:
   $$f(t) = 1100(1.0905)^t$$

   Step4: Calculate hourly growth percentage

   Subtract 1 from the growth factor and convert to percentage:
   $$(1.0905 - 1) \times 100 = 9.05\%$$

3. Final answer

   Function: $f(t) = 1100(1.0905)^t$
   Growth: $9.05$ % increase per hour

答案

Question Analysis

OCR Text

in a lab experiment, 1,100 bacteria are placed in a petri dish. the conditions are such that the number of bacteria is able to double every 8 hours. write a function showing the number of bacteria after $t$ hours, where the hourly growth rate can be found from a constant in the function. round all coefficients in the function to four decimal places. also, determine the percentage of growth per hour, to the nearest hundredth of a percent.
answer
function: $f(t) = \\square(\\square)^\\square$
growth  $\\square$ % increase per hour

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