<h3>Given</h3>
p'(t) = kp²
p(0) = 12; p(10) = 24
<h3>Find</h3>
a) p(t)
b) t such that p(t) = 48
c) the behavior of p(t) after the time of part b
<h3>Solution</h3>
a) The differential equation is separable, so can be solved by separating the variables and integrating.
Plugging in the given boundary conditions, we can solve for k and C to find
b) The population doubles when the time to t=20 is cut in half. The first doubling occurred in 10 years; the second one will occur in half that time, 5 years. There will be 48 alligators in the swamp in 2003.
c) The population doubles again in half the time of the previous doubling, so is predicted to be infinite in 2008.
The distrance to be travelled is 8/10 - 2/25 therefore:
Total dlistance = 81/10 - 12/5
add using least common denominator:
Total distance = 81 - 12 x 2
10
evaluate: Total distance = 57/10 = 5.7
according to the given information if they travel at a speed of 3 miles per house and there are 12-10= 2 hours, so the distance travelled to noon will be 2x = 6 miles - 5.7 miles. This implies that they will be able to reach the 8 1/10 mark by noon.
B the answer is B
C the answer is C
24.65 also next time just use a calculator
The .mp3 player finally sells for $99.00 .
Original price . . . $100 .
Increase the original price by 10% .
(multiply by (100% + 10%) = 110% = 1.10)
(1.10) x ($100) = $110 .
Now decrease the $110 by 10% .
(multiply by (100% - 10%) = 90% = 0.90)
(0.90) x ($110) = $99 .