Answer:
2 hours: 3968 <u>[I don't understand the $ sign in the answer box]</u>
At midnight: 12137
Step-by-step explanation:
The bacteria are increasing by 15% every hour. So for every hour we will have what we started with, plus 15% more.
The "15% more" can be represented mathematically with (1 + 0.15) or 1.15. Let's call this the "growth factor" and assign it the variable b. b is (1 + percent increase).
Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450
At the end of the second hour we're increased by 15% again:
(3450)*(1.15) = 3968.
Each additional hour add another (1.15) factor, If we assign a to be the starting population, this can be represented by:
P = a(1.15)^t for this sample that increase 15% per hour. t is time, in hours.
If a represents the growth factor, and P is the total population, the general expression is
P = ab^t
Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM. That is a 10 hour period, so t = 10
P = (3000)*(1.15)^10
P = 12137
Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
Answer: $139390 must be paid back.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = amount to be played back at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount borrowed.
From the information given,
P = 41000
r = 8.5% = 8.5/100 = 0.085
n = 1 because it was compounded once in a year.
t = 15 years
Therefore,
A = 41000(1 + 0.085/1)^1 × 15
A = 41000(1 + 0.085)^15
A = 41000(1.085)^15
A = $139390
I got:
<span>y′=(−y<span>e^−x</span>−e^y)/xe^y+e^x</span>
then plugged in x and y and got slope of (-5-e^5)
and ended with equation of y=(-5-e^5)x+5
I'm not sure with my solution though i hope this might help you.
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
