Oliver and Paula both read the same book. Paula started reading after Oliver had already read 30 pages.
2 answers:
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Answer:
Step-by-step explanation:
This is an exponential function. In order to find the answer to the question, we need to first determine what the equation is that models this information. The standard form for an exponential function is
where a is the initial value and b is the growth/decay rate. If the starting population is 5000, then
a = 5000
If the population is growing, that means that it retains 100% of the initial population and is added to by another 3.5%. So in a sense the population grows 100% + 3.5% = 103.5% or, in decimal form, 1.035. So
b = 1.035
Our function is
where y is the ending population and x is the number of years it takes to get to that ending population. We want to know how long, x, it will be til the population reaches 7300, y.
and we need to solve for x. The only way to do that is by using logs. I'll use natural logs for this.
Begin by dividing both sides by 5000 to get
and take the natural log of both sides:
The power rule for natural logs is that we can now bring the exponent down in front of the ln to get:
To solve for x, we now divide both sides by ln(1.035):
Do that division on your calculator and get that
x = 11.0 years.
That means that 11 years after the population was 5000 it will be expected to reach 7300 (as long as the growth rate remains 3.5%)
Answer:
Distance: 435.9 ft
Step-by-step explanation:
This is a right triangle shown in the picture.
To solve for , we can use trigonometry.
The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is (what we are seeking to find).
The ratio that relates opposite and hypotenuse is sine.
<em>We know that,</em>
<em>Thus we can write:</em>
<em>Cross multiplying and solving for gives us:</em>
Second answer choice is right: 435.9 ft