Mathematics

How do I do these?

1. Simplify using only positive exponents:

(2t)⁻⁶

2. Simplify using only positive exponents:

(w⁻²j⁻⁴)⁻³(j⁷j³)

3. Simplify using only positive exponents:

a²b⁻⁷c⁴
----------
a⁵b³c⁻²

4. Evaluate the expression for m = 2, t = -3, and z = 0.

z⁻ᵗ(mᵗ)ᶻ

5. Use scientific notation to rewrite the number:
a. 0.0002603 in scientific notation
b. 5.38 × 102 in standard notation

6. The speed of sound is approximately 1.2 × 10³ km/h.
How long does it take for sound to travel 7.2 × 10²

7. Evaluate the function below over the domain {-1, 0,
1, 2}. As the values of the domain increase, do the
values of the function increase or decrease?

y = (3/4)ˣ

8. Suppose an investment of \$5,000 doubles every 12
years. How much is the investment worth after 36
years? After 48 years?
Write and solve an exponential equation.

9. Does the function represent exponential growth or
exponential decay? Identify the growth or decay
factor.

= 9 ∙ (1/2)ˣ

10. You deposit \$520 in an account with 4% interest
compounded monthly. What is the balance in the
account after 5 years?

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1. Happy to check or help, but not to do the problems for you.

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2. I understand, I'm asking how to do them though, not to be done for me. :)

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3. for example

2. Simplify using only positive exponents:

(w⁻²j⁻⁴)⁻³(j⁷j³)

(w^-2 j^-4)^-3 = w^6 j^12
multiply by j^10
w^6 j^22
rules
a^-x = 1/a^x
(a^x)^y = a^(xy)
a^x a^y = a(x+y)

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4. example 10
10. You deposit \$520 in an account with 4% interest
compounded monthly. What is the balance in the
account after 5 years?
4% per year is .04/12 = .0033333 per month
every month multiply by
1.0033333
do that for 60 months which is 5 years
520 * 1.0033333^60
= 520 * 1.221
= 634.92

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5. 9. Does the function represent exponential growth or
exponential decay? Identify the growth or decay
factor.

= 9 ∙ (1/2)ˣ

(1/2)^1 = 1/2
(1/2) ^2 = 1/2^2 = 1/4
(1/2)^3 = 1/2^3 = 1/8 is this getting bigger or smaller ?
(1/2)^x = 1/2^x

(1/2)^x = e^(kx)
x ln .5 = k x
k = ln .5 = -.6931
so in standard exponential notation this is
9 e^-.6931 x
see
https://www.mathsisfun.com/algebra/exponential-growth.html

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