John has a bag of different colored marbles. He has 6 red marbles, 3 blue marbles, 7 yellow marbles, and 5 green marbles If John
2 answers:
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Answer:
Part a)
Part b)
Step-by-step explanation:
Part a) Create a linear equation
Let
t ----> the time in minutes
y ---> the temperature in °F
we know that
The linear equation in slope intercept form is equal to
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
In this problem we have
The slope m is equal to
The y-intercept is
substitute
Part b) How many minutes until the water boils at 212° F?
For y=212° F
substitute in the linear equation and solve for t
Answer:
1. The equation represent an exponential decay
2. The rate of the exponential decay is -3×2.5ˣ·㏑(2.5)
Step-by-step explanation:
When a function a(t) = a₀(1 + r)ˣ has exponential growth, the logarithm of x grows with time such that;
log a(t) = log(a₀) + x·log(1 + r)
Hence in the equation -3 ≡ a₀, (1 + r) ≡ 2.5 and y ≡ a(t). Plugging in the values in the above equation for the condition of an exponential growth, we have;
log y = log(-3) + x·log(2.5)
Therefore, since log(-3) is complex, the equation does not represent an exponential growth hence the equation represents an exponential decay.
The rate of the exponential decay is given by the following equation;
Hence the rate of exponential decay is -3×2.5ˣ × ㏑(2.5)