Hi there!
We know that:
U = Potential Energy (J)
K = Kinetic Energy (J)
E = Total Energy (J)
At 10m, the total amount of energy is equivalent to:
U + K = 50 + 50 = 100 J
To find the highest point the object can travel, K = 0 J and U is at a maximum of 100 J, so:
100J = mgh
We know at 10m U = 50J, so we can solve for mass. Let g = 10 m/s².
50J = 10(10)m
m = 1/2 kg
Now, solve for height given that E = 100 J:
100J = 1/2(10)h
100J = 5h
<u>h = 20 meters</u>
In order to find out if the exponential function represents a growth or a decay, let's look at the number that is base to the exponent x.
If the number is greater than 1, so the function represents a growth, and if the number is less than 1, the function represents a decay.
Since the number is 1.075, the function represents a growth.
To find the % increase, first let's convert the number to percentage, and then subtract 100%:
So the percent increase is 7.5%.