The function that models exponential growth is:
P(t) = P0*(1 + r)^t, where
P0 = P(0) is the initial value of P
r is the growth rate as a decimal
In our case we have:
P(0) = 2800
r = 0.035 or 3.5%
P(t) = 2800*(1 + 0.035)^t
P(t) = 2800*(1.035)^t
The same exponential function written using y and t is:
y = 2800*1.035^t.
Explanation: https://softmath.com/algebra-word-problems/to-begin-a-bacteria-study-a-petri-dish-had-2800-bacteria
Answer:
Pyramid
V= 240 m^3
Step-by-step explanation:
The volume of a pyramid is 1/3 the Base times the height.
1/3x(10x8)x9
Answer: 80 feet
Step-by-step explanation:
We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:
5 * 128 = 8x
640 = 8x
80 = x
Thus, the height of the lighthouse is 80 feet tall.
<span>1,
During a 1-hr television program, there were 22 commercials, Some
commercials were 15 sec and some were 30 sec long. Find the number of
15- sec commercials and the number of 30 sec commercial if the total
playing time for commercial was 9.5 minutes.
</span>a) <span>show how to formulate your system of equations for your problem,
Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language
b) state the two equations:
- translate the word statement into algebraic equations:
</span><span>* there were 22 commercials => x + y = 22
* the total playing
time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>
Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570
c) state which method you will use to solve either addition or substitution
Answer:
adition: multiply the first equation times - 15 and add the two equations.
d) solve your system showing and explaining each step of the process
Answer:
- muliply eq (1) times - 15
-15x - 15y = - 330
- add that to the eq (2):
-15x + 15x - 15y + 30y = -330 + 570
- add like terms: 15y = 240
- divide both members by 15: 15y/15 = 240 / 15 => y = 16
- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6
Solution: x = 6, y = 16
e) Be sure to check your solution!
x + y = 22
6 + 16 = 22
22 = 22 --> check
15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check
f) Once a solution is found explain what this solution means in the context
of the problem, write the answer to the word problem in words</span><span>
The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.
2, How many quarts of water should be mixed with a 30% vinegar solution
to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>
a) variables:
- state the variables
x: number of quarters of water
y: number of quarters of vinegar
- translate the words into mathematical language
12 qt 25% vinegar solution
=> total number of quarts = 12 = x + y
balance in vinegar:
vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution
0 + 0.3y = 0.25 (x + y)
c) Equations
Eq (1) x + y = 12
Eq (2): 0.3y = 0.25x + 0.25y
=> 0.25x - 0.05y = 0
d) solve
- multiply eq (1) times 0.05 and add to eq (2)
0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6
x = 0.6 / 0.3 = 2
x + y = 12 => y = 12 - y = 12 - 2 = 10
Solution: x = 2, y = 10
e) check:
x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check
vinegar:
10*0.3 = 12*0.25
3 = 3 -> check
f) Explanation of the solution
The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.
Answer:
80.95
Step-by-step explanation:
Percentage increase = 
*100
=> (38-21)* 100/21 = 80.9523%
The answer round it to the nearest 100th = 80.95%
