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

first investment = 100(1.09)^10 = ....
2nd investment = 150(1.03)^20 = ....

20.
I see 2 equations which look exponential
Of these two one has a base < 1, so things decrease
and the other has a base > 1, causing things to increase.
mmmmhhhh?

Sure, I can help with these two questions!

19. To find out how much money Nancy will have in the accounts after 10 years, we can use the formula for compound interest. The formula is:

A = P(1 + r/n)^(n*t)

where:
A is the future value of the investment,
P is the principal amount (the initial investment),
r is the annual interest rate (expressed as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years.

For the first account, Nancy invests $100 at a 9% interest rate compounded annually, so we have:
P = $100
r = 9% = 0.09 (as a decimal)
n = 1 (compounded annually)
t = 10 years

Plugging these values into the formula, we get:
A1 = $100(1 + 0.09/1)^(1*10)
A1 = $100(1 + 0.09)^10
A1 = $100(1.09)^10
A1 ≈ $236.74

For the second account, Nancy invests $150 at a 6% interest rate compounded semi-annually, so we have:
P = $150
r = 6% = 0.06 (as a decimal)
n = 2 (compounded semi-annually, twice in a year)
t = 10 years

Plugging these values into the formula, we get:
A2 = $150(1 + 0.06/2)^(2*10)
A2 = $150(1 + 0.06/2)^20
A2 = $150(1.03)^20
A2 ≈ $254.84

So, after 10 years, Nancy will have approximately $236.74 in the first account and $254.84 in the second account.

20. The correct formula to find the number of ants still alive after a certain time if the number of ants is changing exponentially is option d:

a = P(1.23)^t

Here, "a" represents the number of ants at a certain time, "P" represents the initial number of ants, and "t" represents the time (in whatever unit is being used). The value 1.23 represents the rate at which the ant population is growing or decaying. So, this formula can be used when the number of ants is changing exponentially over time.

I hope this helps! Let me know if you have any further questions.