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DedPeter [7]
3 years ago
9

the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what

year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009
Mathematics
2 answers:
dangina [55]3 years ago
4 0
4=1.1e^(0.047t)  divide both sides by 1.1

40/11=e^(0.047t)  take the natural log of both sides

ln(40/11)=0.047t  divide both sides by 0.047

t=ln(40/11)/0.047

t≈24.5

1980+24.5

2007.5

So during 2007 the price will reach $4.

OverLord2011 [107]3 years ago
3 0

Answer:

The option A.) 2007 is correct

Step-by-step explanation:

The formula which is to be used is given :

P(t) = 1.1\cdot e^{0.047t}

where P(t) is the function of time t and t is the time in years after January 1 , 1980

Now, we need to find the year when the price will reach $4

So, substituting P(t) = 4 and finding the value of t from the given equation.

\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49

So, t = 27.49 which is approximately equals to 27.5 years

So, 27.5 years after January 1, 1980 is the year 2007

Hence, The price will reach $4 in the year 2007

Therefore, The option A.) 2007 is correct

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tresset_1 [31]
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5 0
3 years ago
A family is planning a three-week vacation for which they will drive across the country. They have a van that gets 12 miles per
svetoff [14.1K]

Answer:

The family will pay 34722 cents more if they take the van

Step-by-step explanation:

Given

Van = 12 miles per gallon

Sedan = 36 miles per gallon

Distance = 2500 miles

Gas = $2.50 per gallon

First, we need to determine the number of gallons that'll be used by both vehicles

This  is done by dividing total distance by number of miles per gallon

Van = \frac{2500}{12} \ gallon

Sedan = \frac{2500}{36}\ gallon

Next, is to multiply this by the cost of gas per gallon;

This gives the total spendable amount on both vehicles

Van = \frac{2500}{12} * \$2.50

Van = \frac{\$6250}{12}

Van = \$520.833

Sedan = \frac{2500}{36}* \$2.50

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Sedan = \$173.611

Next is to get the difference between these amounts

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Difference = \$347.222

Multiply by 100 to convert to cents

Difference = 347.222 * 100 cents

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Hence;

<em>The family will pay 34722 cents more if they take the van</em>

8 0
2 years ago
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LekaFEV [45]

Answer:

600 volts

Step-by-step explanation:

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A = 12 ampere

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7 0
3 years ago
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madam [21]

Answer:

A fair six-sized die is rolled. Find the probability of getting at least a 4.

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5 0
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Answer:

x = -15

Step-by-step explanation:

x - 15 = -30

add 15 to both sides

x = -15

4 0
3 years ago
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