Sum of a finite geometric series=a(r^(n) -1)/(r -1)
or
sum of a finite geometric series=a(1 - r^(n))/(1 - r)
the Smiths would spend a total of $2928.2 on clothing in 4 years
I think the answer is that what i think
<u>Answer:</u>
<u>Step-by-step </u><u>Explanation</u><u>:</u>
The sequence is following some rule. And the rule is: Multiplying the term with 4 to get the next term. Like:
Similarly, the next terms are:
The terms are <u>6</u><u>4</u><u>,</u><u> </u><u>2</u><u>5</u><u>6</u><u>,</u><u> </u><u>1</u><u>0</u><u>2</u><u>4</u> which matches with Option D. And that's the correct answer
From the calculation, the growth rate is 0.88.
<h3>What is the growth rate?</h3>
To find the relative growth rate
P1 = Poe^rt
P2 = Poe^rt
Thus;
1920 = Poe^4r ------ (1)
1966080 =Poe^12r -------(2)
P2/P1 gives;
1966080/1920 = Poe^12r/Poe^4r
1024 = e^12r/e^4r
1024 =e^8r
1024 = (e^r)^8
2^10 = (e^r)^8
e^r = 2^1.25
e^r = 2.38
r = ln(2.38)
r = 0.88
The initial size of the culture is;
1920 = Poe^(0.88 * 4)
Po = 1920/e^(0.88 * 4)
Po = 57
The expression for the exact number of bacteria after t hours is
P(t) = 57e^0.08t
The growth (in bacteria per hour) after 9.5 hours is
P(t) = 57e^(0.88 * 9.5)
P(t) = 243544
For the number to reach 72,000;
72,000 = 57e^0.88t
72,000/57 = e^0.88t
ln 126 = ln[e^0.88t]
4.8 = 0.88t
t = 4.8/0.88
t = 5.5 hours
Learn more about exponential growth;brainly.com/question/13674608
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