What is the answer its for a grade
1 answer:
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Given:
The function is
where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
To find:
Number of complex and real zeros.
Time intervals for which the population increased and population deceased.
Solution:
We have,
Here, degree of function x is 3. It means, the given function has 3 zeros.
From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.
So, the given function r(x) has only one real root and other two real roots are complex.
Therefore, function r has 2 complex zeros and one real zero.
Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.
Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.
Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.
Answer:
a) 8.16%
b) $65,762.50
c) $39,701.07
Step-by-step explanation:
Given:
15 years ago, Initial investment = $12500
5 years ago, Investment = $20000
Nominal interest = 8% semi annually for first 10 years
Interest2= 6.5% compunded annually for last five years
a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:
[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1
= 1.0816 - 1
= 0.0816
= 8.16%
The effective annual interesting rate, EAR = 8.16 %
b) To find the amount in my account today.
Let's first find the amount for $12500 for 10 years compounded semi annually
= 12,500 +( 12,500 * 8.160% * 10)
= $ 22,700
Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually
$32,500 + ($32,500 * 6.5% *5)
= $ 43,062.50
Money in account today will be:
$22,700 + $43,062.50
= $65,762.50
c) Let's the amount I should have invested to be X
For first 10 years at 8.160%, we have:
Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X
For next 5 years at 6.5%, we have:
Interest Amount = (X * 6.5% * 5) = 0.325 X
Therefore the total money at the end of 15 Years = 85000
0.8160X + 0.3250X + X = $85,000
= 2.141X = $85,000
X = 85,000/2.141
X = 39,701.074 ≈ $39,700
If I wish to have $85,000 now, I should have invested $39,700 15 years ago