I'm really stuck on these 2. Can you please explain the work clearly so that I can understand and find the answer easily, if already not given.
Need help with these 2 please--
19. Nancy invests $100 in one account for 10 years at a 9% interest rate compounded annually, and she invests $150 in an account for 10 years at a 6% interest rate compounded semi-annually. How much money will she have in the accounts after 10 years?
20. Suppose Tyler sprayed around the house for ants. Which formula would be used to find the number of ants still alive after a certain time if the number of ants was changing exponentially?
a. a = P(o.56)^t
b. y = mx + b
c. a = x
d. a = P(1.23)^t
Thanks
-MC
19. Pt=Po(r+1)^n =100(1.09)^10=236.74
n=the number of compoundingperiods.
r=Rate per compounding period=APR.
Po=amount invested.
Pt=amount at 10 yrs.
Pt=150(1.03)^20=270.92
TOTAL=236.74++270.92=507.16
20. The correct choice is d.
a is not the correct choice,becaus
when a number less than one is
raised to a power ,it decreases.
To solve both of these problems, let's break them down step by step:
19. To find the amount of money Nancy will have in the accounts after 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount of money after t years
P = the initial principal (amount invested)
r = the interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, Nancy invests $100 in an account for 10 years at a 9% interest rate compounded annually, and $150 in an account for 10 years at a 6% interest rate compounded semi-annually.
For the first account, plug in the values into the formula:
P = $100, r = 9% (or 0.09), n = 1 (compounded annually), t = 10
A = 100(1 + 0.09/1)^(1*10)
A = 100(1.09)^10
A ≈ $236.59
For the second account, plug in the values into the formula:
P = $150, r = 6% (or 0.06), n = 2 (compounded semi-annually), t = 10
A = 150(1 + 0.06/2)^(2*10)
A = 150(1.03)^20
A ≈ $311.01
Therefore, Nancy will have approximately $236.59 + $311.01 = $547.60 in both accounts after 10 years.
20. In this problem, we need to choose the formula that represents the number of ants still alive after a certain time when the number of ants is changing exponentially.
The correct formula in this scenario would be option d. a = P(1.23)^t, where:
a = the number of ants after time t (the variable we want to find)
P = the initial number of ants
t = time passed
This formula represents exponential growth, where the number of ants is increasing over time.
Therefore, for finding the number of ants still alive after a certain time, you would use formula d. a = P(1.23)^t.