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

to answer number 19,

100(1+.09/1)^1x10 = 236

150(1+.06/2)^2x10 = 270

236+270= 506$
answer: 506$

19. To calculate the amount of money Nancy will have in the accounts after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the initial principal (amount invested)
r = interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = time in years

For the first account, Nancy invested $100 at a 9% interest rate, compounded annually. Plugging in the values we have:

P = $100
r = 9% or 0.09 (converted to decimal)
n = 1 (since it is compounded annually)
t = 10 years

Using the formula:

A1 = $100(1 + 0.09/1)^(1*10)
A1 = $100(1.09)^10
A1 ≈ $235.79 (rounded to the nearest cent)

For the second account, Nancy invested $150 at a 6% interest rate, compounded semi-annually. This means interest is compounded twice per year. Plugging in the values we have:

P = $150
r = 6% or 0.06 (converted to decimal)
n = 2 (since it is compounded semi-annually)
t = 10 years

Using the formula:

A2 = $150(1 + 0.06/2)^(2*10)
A2 = $150(1.03)^20
A2 ≈ $253.95 (rounded to the nearest cent)

Therefore, Nancy will have approximately $235.79 + $253.95 = $489.74 in the accounts after 10 years.

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

d. a = P(1.23)^t

Where:
a = the number of ants still alive
P = the initial number of ants
t = time in years
1.23 = a constant specific to the rate of decline or growth of the ant population

In this case, option d is the correct formula.