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Differentiation
This question causing me quite a few difficulties and I've got answer wrong so many times that I need help.
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
a) find an expression for t in terms of P and P0
Answer: (ln P-ln P0)/ln 1.09
b) Find the time T years when the population has doubled from its value at t=0 giving your answer to 3.s.f
Answer:8.04 years
c) Find, as a multiple of P0, the rate of change of population dP/dt at time t=T.
Answer: 0.172P0
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
a) find an expression for t in terms of P and P0
Answer: (ln P-ln P0)/ln 1.09
b) Find the time T years when the population has doubled from its value at t=0 giving your answer to 3.s.f
Answer:8.04 years
c) Find, as a multiple of P0, the rate of change of population dP/dt at time t=T.
Answer: 0.172P0
mala2k
This question causing me quite a few difficulties and I've got answer wrong so many times that I need help.
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
a) find an expression for t in terms of P and P0
Answer: (ln P-ln P0)/ln 1.09
b) Find the time T years when the population has doubled from its value at t=0 giving your answer to 3.s.f
Answer:8.04 years
c) Find, as a multiple of P0, the rate of change of population dP/dt at time t=T.
Answer: 0.172P0
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
a) find an expression for t in terms of P and P0
Answer: (ln P-ln P0)/ln 1.09
b) Find the time T years when the population has doubled from its value at t=0 giving your answer to 3.s.f
Answer:8.04 years
c) Find, as a multiple of P0, the rate of change of population dP/dt at time t=T.
Answer: 0.172P0
P=Po(1.09)t ..............(*)
ln P=ln[Po(1.09)^t]
ln P=ln Po+tln(1.09)
[lnP-lnPo]/(ln(1.09)=t
when t=0 P=Po we need time t=T when P=2Po
T=ln(2Po)-ln(Po)/ln(1.09)
=ln2/ln(1.09)
=8.04
from
[lnP-lnPo]/(ln(1.09)=t
have 1/PdP/dt=ln(1.09)
=>dP/dt=ln(1.09)[p0(1.09)^t] ..................(using *)
at T=8.04
dP/dt=Po(.0861776)(1.99943)
=0.1723Po
This question causing me quite a few difficulties and I've got answer wrong so many times that I need help.
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
C4 Heinmann Book Mixed excercise 4F question 21
A population P is growing at a rate of 9% each year and at time t years may be approximiated by the formula:
P=P0(1.09)t Where t=>0 (t is greater then or equal to zero)
where P is regarded as a continuous function of t and P0 is the starting population at time t=0.
a) find an expression for t in terms of P and P0
P = P0(1.09)t
Take logarithms of both sides.
lnP = lnP0(1.09)t
lnP = lnP0 + ln(1.09)t
lnP = lnP0 + tln(1.09)
t = (lnP - lnP0)/ln1.09
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