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The count in a bacteria culture was 200 after 15 minutes and 1500 after 40 minutes. What was the initial size of the culture? Find the doubling period. Find the population after 120 minutes. When will the population reach 11000.
Solve each equation for x. (a) 5^(x−5)=2 (b) lnx+ln(x−1)=1?
Find (a) the domain of f and (b) f−1.
f(x)=ln(2+lnx)

(a) x>............
(b) f−1(x)=...........
Which of the following illustrates how the graphs of y=a^x and y=a^(−x) with a>1 are related?
(a) One is a reflection over the x-axis of the other.
(b) One is a reflection over the y-axis of the other.
(c) Both (a) and (b).
(d) None of the above.
Which of the following explains how to obtain the graph of y=2+5(1+e^(−x)) from the graph of y=e(−x)?
(a) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result up 2 units.
(b) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result down 2 units.
(c) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result up 7 units.
(d) Vertically stretch the graph of y=e^(−x) by a factor of 5 and then shift this result down 7 units.
prove that : (V final)^2 = (V initial)^2 + 2aS ..... (( using calculus 'integration' ))
When can you have a first derivative that's undefined and second derivative that's zero?
find the asymptotes of following curves x^3-2y^3+xy(2x-y)+y(x-1)+1=0
and
x^3-5x^2y+8xy^2-4y^3+x^2-3xy+2y^2-1=0
solve it step by step. thank you.
A series of circles have their centres on a given straight line and their radii proportional tothe distances
of their corresponding centres from a given point in that line .find the envelope.plz solve this question step by step.
from any point on ellipse x^2/a^2+y^2/b^2=1 perpendiculars are drawn to the axis.show that the line joining the feet of perpendiculars always touches the curve
(x/a)^2/3+(y/b)^2/3=1
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