Answer:
Step-by-step explanation:
This is of the form
Where P(t) is the ending population, a is the original population, b is the growth rate, and t is time in years. We have everything we need to solve for t.
Let me explain the growth rate quickly. If the exponential function is a growth function, that means (in this particular situation) that we have 100% of the population and we are increasing it by 19%. That makes the growth rate 119%, which in decimal form is 1.19.
Begin by dividing both sides by 40000 to get
To get that t out of its current exponential position, take the natural log of both sides:
and the rules of logs say we can bring the exponent down out front:
ln(2) = t*ln(1.19)
Divide both sides by ln(1.19) to get t alone:
Doing that calculation on your calculator gives you that
t = 3.9846...
but rounding to the nearest tenth gives you that
t = 4.0 years
1 unit left and reflection across x axis
Answer:
ti is m(B{AC=70*
Step-by-step explanation:
Step-by-step explanation:
Top answer · 0 votes
f(g(x))=362−x−2k f(g(x))=x→362−x−2k=x→x2−2x(1−k)−4(k−9)=0 Solution for x are equal if and only if discriminant Δ=0 4(1−k)2+16(k−9)=0 ... More
Recall that
sin(<em>a</em> + <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) + cos(<em>a</em>) sin(<em>b</em>)
sin(<em>a</em> - <em>b</em>) = sin(<em>a</em>) cos(<em>b</em>) - cos(<em>a</em>) sin(<em>b</em>)
Adding these together gives
sin(<em>a</em> + <em>b</em>) + sin(<em>a</em> - <em>b</em>) = 2 sin(<em>a</em>) cos(<em>b</em>)
To get 14 cos(39<em>x</em>) sin(19<em>x</em>) on the right side, multiply both sides by 7 and replace <em>a</em> = 19<em>x</em> and <em>b</em> = 39<em>x</em> :
7 (sin(19<em>x</em> + 39<em>x</em>) + sin(19<em>x</em> - 39<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) + sin(-20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
7 (sin(58<em>x</em>) - sin(20<em>x</em>)) = 14 cos(39<em>x</em>) sin(19<em>x</em>)
