The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.
1 answer:
Answer:
Step-by-step explanation:
The lion population in a certain reserve drops by 5\%5%5, percent every year. Currently, the population's size is 200200200.
Write a function that gives the lion population size,
Each year, the population drops to 95% of its previous value. (100 - 5)%
That is, the population is multiplied by 0.95 each year.
Repeated multiplication is signified by an exponent.
Here, that exponent is the number of years from today (t).
<h3>There fore, The population function can be written as ...</h3><h3 /><h3> P(t) = 200·0.95^t</h3><h3>You might be interested in
Answer:
a) t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
b) x = 0,97 miles
c) t (min) = 1,24 hours
Step-by-step explanation: See Annex
Figure in annex shows a clear description of the situation
Let x be distance in miles between point P and where boat lands
A woman has to row a distance L
L = √ (4)² + (x)²
and the part to get to the town (which she has to walk)
d = ( 7 - x)
But we are required to give time as a function of x
distance = speed * time ⇒ t = distance / speed
Therefore
t(x) = [ √ (4)² + (x)²]/ 4 + ( 7 - x ) / 5
t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
Taking derivatives both sides of the equation
t¨(x) = ( 2x)*4 / 16√ (4)² + (x)²] - 5/25
t¨(x) = x/ 2√ (4)² + (x)²] - 1/5
t¨(x) = 0 x/ 2√ (4)² + (x)²] - 1/5 = 0
[ 5 x - 2√ (4)² + (x)²] = 0 ⇒ 5x = 2√ (4)² + (x)²] or
25 x² = 4 ( 4 + x²)
25 x² = 16 + 8x²
17x² = 16
x² = 16/17
x² = 0,941
x = 0,97 miles
And the distance walking to get to town
d = 7 - x d = 7 - 0,97
d = 6,03 miles
The least travel time is t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
t (min) = √ 16 + 0,94) /4 + 1,4 - 0,97/5
t (min) = 1,03 + 1,4 - 0,194
t (min) = 1,24 hours
Solution:
As we are given that f(1) = 0 .
It mean that is one of the factor of the given equation.
Remainder theorem can be applied as below:
Hence the factors are (x-1),(x+3) and (x+1).
Hence the correct option is B.