Tia invests $2,500 at an interest rate of 4%, compounded quarterly, and another $2,500 at an interest rate of 3.75%, compounded annually. How much are the investments worth at the end of 5 years

Use formula for intrested compunded continuously which is ...

A = Pe^(rt)

A = Total Balance you will receive

P = Principal (amount you start out with)

e = The constant e (2.71818... can be foudn on your calculator)

r = Rate (Remember to convert to decimal form out of a whole)

t = Time

Lets assemble the equation for balance after 1 year...

A = 2000e^(.06x1)

A = $2123.67

So after 1 year, your balance is $2123.67

To find balance after 2 years, just substitute (t) for 2

A = 2000e^(.06x2)

A = $2254.99

After 2 years, your balance is $2254.99

Hope this helps

EDIT for the sake of clarifying what compounding continuously means, compared to compounding annually, semi annually, quarterly, etc... etc (I will try my best)

Continuous compounding can be thought of as making the compounding period infinitesimally small; therefore achieved by taking the limit of n to infinity.

Think of it as compounding continuously is an asymptote, you can compound annually, semi annually, quarterly, monthly, daily, even per second. Going down this progressive series approaches this asymptote which increasingly gets smaller but never crosses, so we substitute it with infinity. The asymptote is what we are compounding and can be found with A = Pe^(rt)

Step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have