Exponential growth/decay rule with general function is:<span>y=y(0)<span>e<span>kt</span></span></span>
with k is growth/decay constant rate.
(1) Deer population function
y(0) = 1253
k
= 3%
t
= 6 (years)
y(6) = 1253 . e^(0.03*6) ~ 1500 (deers)
: 1496 deers
(2) Growth factor b is rate 9.5% = 0.095
35,37,39
111 divided by 3 is 37...so that is the middle number. Two below it is 35 and 2 above it is 39 and all three would add up to 111. So 35 is the lowest.
Given equations are;<span>
2a + 3b = -1 ..................equation 1
3a + 5b = -2 ....................equation 2</span>
Now multiply equation 1 with (-3)
The equation will be;
-6a -9b = 3 …………………..equation 3
Now multiply equation 2 with (2)
The equation will be;
6a + 10b = -4 ……………..equation 4
Now add equation 3 and equation 4
-6a – 9b = 3
<span>6a + 10b = -4</span>
<span>------------------------------</span>
0a + b = -1
b = -1
Now put the value of b in equation 1
2a + 3(-1) = -1
2a -3 = -1
2a = -1+3
2a = 2
a=1
Thus the solution is (a,b) = (1,-1)
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You can cross multiply and the answer would be 100/9
9/10=10/k
100=9k
k=100/9
