Question

After t hours there are P(t) cells present in a culture, where: P(t) = 3400e⁰.⁴ᵗ 1. How many cells were initially present?. P(0) = cells. 2. What is the growth constant? k= 3. When will the initial number of cells double?. t= hours 4. When will 13600 cells be present? t= hours

Answer 1

The initial number of cells is 3400. The growth constant is 0.4. The time it takes for the initial number of cells to double or for 13600 cells to be present can be found using logarithms.

Step-by-step explanation:

1. To find the initial number of cells, we can substitute t=0 into the equation P(t) = 3400e⁰.⁴ᵗ. This gives us P(0) = 3400e⁰, which simplifies to P(0) = 3400 cells.

2. The growth constant can be found by examining the exponent in the equation P(t) = 3400e⁰.⁴ᵗ. In this case, the growth constant is 0.4.

3. To find when the initial number of cells double, we need to solve the equation 2P(0) = 3400e⁰.⁴ᵗ for t. Using logarithms, we can solve for t and find that t = ln(2)/0.4.

4. To find when 13600 cells will be present, we need to solve the equation 13600 = 3400e⁰.⁴ᵗ for t. Again, using logarithms, we can solve for t and find the approximate value of t.

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