Which logarithmic graph can be used to approximate the value of y in the equation 4^y = 8?
1 answer:
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Answer:
Step-by-step explanation:
Given equation can be re written as
............(i)
Now it is given that y(π/2) = 2e
Applying value in (i) we get
ln(2e) = sin(π/2) + c
=> ln(2) + ln(e) = 1+c
=> ln(2) + 1 = 1 + c
=> c = ln(2)
Thus equation (i) becomes
ln(y) = sin(x) + ln(2)
ln(y) - ln(2) = sin(x)
ln(y/2) = sin(x)
Answer:
$9000 at 4$
and
$10000 at 8%
Step-by-step explanation:
Let's assume that "x" is the amount deposited in the 4% account and "y" is the amount deposited in the 8% account.
Recall the formula for interest as :
where I is the interest, R is the annual rate of interest and t is the number of years.
Since there are two investments, we need to add both interests at the end of the one year: I1 = x (0.04) (1) = 0.04 x and I2 = y (0.08) (1) = 0.08 y
Total Interest = Interest (from the 4% account) + Interest (from the 8% account)
Total Interest = $1160 = 0.04 x + 0.08 y
we also know that the total invested (x + y) adds to $19,000, that is:
$19,000 = x + y
Then we can solve these system of two equations by substitution, for example solving for y in the second equation and using the y substitution in the first equation;
y = 19000 - x
1160 = 0.04 x + 0.08 (19000 - x)
1160 = 0.04 x + 1520 - 0.08 x
0.08 x - 0.04 x = 1520 - 1160
0.04 x = 360
x = 360/0.04 = $9000
Then the other investment was : y = $19000 - $9000 = $10000