Identify the initial amount a and the growth factor b in the exponential function. f(x) = 620 • 7.8x
2 answers:
Answer:
Initial amount: 620
Growth Factor: 7.8
Step-by-step explanation:
Based on my research the Exponential Growth Formula is the following,
<u>In which:</u>
- f(x) is the total growth after a given time
- a is the initial amount
- r is the rate of growth in decimal form
- t is the unit of time
Based on this information we can deduce that in the exponential function given to us in the question we can say that 620 is our initial amount and 7.8 is our growth factor.
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Answer:
(a) 7.5 seconds
(b) The horizontal distance the package travel during its descent is 1737.8 ft
Step-by-step explanation:
(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀
The initial height of the object s₀ = 900 feet
The initial vertical velocity of the object v₀ = 0 m/s
The time it takes the package to strike the ground is found as follows;
0 = -16·t² + 0×t + 900
900 = 16·t²
t² = 900/16 = 62.25
t = √62.25 = 7.5 seconds
(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have
158 miles/hour = 231.7126 ft/s
The horizontal distance the package covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place
The horizontal distance the package travel during its descent = 1737.8 ft.