Given:
Annual population of butterflies after t years is
To find:
The growth rate.
Solution:
The general exponential function is
...(i)
where, a is initial value, t is time and r is growth rate.
We have,
It can be written as
...(ii)
On comparing (i) and (ii), we get
Initial value : 
Growth rate : 
Therefore, the growth rate is 8.5%.
the multiplication of fractions is very straightforward, numerators across and denominators across, now, let's firstly convert the mixed fraction to improper fraction.
![\bf \stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{5}\cdot \cfrac{5}{7}\implies \cfrac{12}{7}\cdot \cfrac{5}{5}\implies \cfrac{12}{7}\cdot 1\implies \cfrac{12}{7}\implies 1\frac{5}{7}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B2%7D%7B5%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%205%2B2%7D%7B5%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B12%7D%7B5%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B12%7D%7B5%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B7%7D%5Ccdot%20%5Ccfrac%7B5%7D%7B5%7D%5Cimplies%20%5Ccfrac%7B12%7D%7B7%7D%5Ccdot%201%5Cimplies%20%5Ccfrac%7B12%7D%7B7%7D%5Cimplies%201%5Cfrac%7B5%7D%7B7%7D)
Answer:
Step-by-step explanation:
1. 2( 2d + 2)
2.w + 12
3x - 2y = 7
-2y = -3x + 7
y = 3/2x - 7/2....slope of this line is 3/2. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So the slope we need is -2/3 (see how I flipped the slope and changed the sign)
y = mx + b
slope(m) = -2/3
(-3,-2).....x = -3 and y = -2
now we sub and find b, the y int
-2 = -2/3(-3) = b
-2 = 2 + b
-2 - 2 = b
-4 = b
so ur perpendicular equation is : y = -2/3x - 4 <==
