A population, N_{t}, at at time, t, increases by 50% every T = 10 years. If the initial value of N_{0} = 2000, the growth can be represented by the equation N_{t} = 2000×(1.5)^{t/10} Which of the following equations most closely represents the same growth. Hint: When t = 10, the calculated value of N_{t} should be 50% greater than N_{0} = 2000.
N_{t} = 2000×e^{0.018×t}
N_{t} = 2000×e^{0.041×t}
N_{t} = 2000×e^{0.15×t}
N_{t} = 2000×e^{0.80×t}
The decimal reduction time, T_{D}, of a bacterial population is the time it takes to fall to one tenth of its initial value. A dying bacterial population N_{t} with a decimal reduction time, T_{D} = 45 min. can be represented by the equation N_{t} = N_{0}×(0.1)^{t/45} Which of the following equations most closely represents the same growth. Hint: When t = 45 min, the calculated value of N_{t} should be one tenth of N_{0}.
N_{t} = N_{0}×e^{0.022×t}
N_{t} = N_{0}×e^{- 0.022×t}
N_{t} = N_{0}×e^{0.051×t}
N_{t} = N_{0}×e^{- 0.051×t}
The decaying activity, A_{t}, of a radioactive isotope with respect to time, t, can be written as A_{t} = A_{0}×e^{- 0.693×t/T1/2} where T_{1/2} is the half life. Calculate the half-life, T_{1/2}, of an isotope whose activity falls from 8500 Bq to 5300 Bq in 27 days
30.1 days
39.6 days
81.6 days
91.2 days
A population that increases exponentially by a factor ‘g’ in a time T, can be described the equation N_{t} = N_{0}×(g)^{t/T} (e.g. an increase of 10% would give a value of g = 1.1, and a fall by 10% would give a value of g = 0.9) The same exponential behaviour can also be described using the equation N_{t} = N_{0}×e^{k×t} where the value of k can be calculated by using the equation:
k = ln(g) / T
k = ln(g) × T
k = T / ln(g)
None of the above
A disease is spreading exponentially, such that the number of cases, N_{t}, is increasing by 15% every week. If there are 50 cases at the beginning of the first day (when t = 0), which of the following equations most accurately describes the growth in a time t, where t is measured in days.