Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

A)

B)

C)

Step-by-step explanation:

We are given the function:

A)

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

Simplify:

Anything raised to zero (except for zero) is one. Therefore:

B)

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

Simplify:

We can take the natural log of both sides:

By definition, ln(e) = 1. Hence:

Therefore:

C)

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

Simplfy:

Take the natural log of both sides:

Therefore:

Therefore:

i don't have the answer rn but go to math papa. it shows the steps and the answer. hope this : )

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.