Understanding Base e and Natural Logarithms

What happens to the function e^x when the exponent is negative?

• It remains unchanged.

• It becomes a quadratic function.

• It represents exponential decay.

• It becomes a linear function.

Which of the following represents an exponential growth model?

• x^2

• e^(-x)

• ln(x)

• e^(x)

How are the graphs of e^x and ln(x) related?

• They are parallel.

• They are identical.

• They are perpendicular.

• They are symmetric across the line y=x.

What is the equivalent logarithmic form of e^x = 25?

• ln(25) = x

• log(25) = x

• ln(x) = 25

• log(x) = 25

What is the value of ln(e)?

• 0

• 1

• e

• Undefined

Which button on a calculator is used to access the e^x function?

• The exp button

• The log button

• The ln button

• The second function of the ln button

What is the formula used for continuously compounded interest?

• A = P(1 + r/n)^(nt)

• A = P(1 + r)^t

• A = P(1 + rt)

• A = Pe^(rt)

If $700 is deposited at 3% interest compounded continuously, what is the balance after 8 years?

• $910.00

• $888.49

• $900.00

• $885.84

How long will it take for $700 to grow to $1200 at 3% interest compounded continuously?

• 18.3 years

• 20.5 years

• 15.2 years

• 17.9 years

What principal amount must be deposited to reach $1500 in 12 years at 3% interest compounded continuously?

• $1,046.51

• $1,300.00

• $1,200.00

• $1,100.00