15 Points!!!!!!!!! Mike attends basketball practice sessions every week. The coach assesses his progress at the end of each sess
2 answers:
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Answer: Exponential function
Step-by-step explanation:
A linear function is the form , where m is the constant rate of change of y with respect to x and c is the y-intercept.
An exponential growth function is in the form , where r is the rate of growth (generally in percent) and A is initial value.
If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .
Hence it is an exponential equation.
Let's call the two numbers and
.
Given these variables, we can say: , based on the first sentence in the problem.
Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:
To solve, we can simply substitute in for
in the second equation and solve.
- Set up
- Get terms on the left side to a common denominator for easier addition
- Simplify
- Cross multiplication (
)
- Simplify
- Subtract
from both sides of the equation
- Factor left side of the equation
- Zero Product Property
Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,
,
Since is not positive in this case,
is not a solution.
Thus, is our only solution. In this case,
,
which means that the smaller number is 14 and the larger number is 28.