Question

1.A Five hours after the start of an experiment, there were 700 bacteria, and 4 hours after that there were 1200 bacteria. Write a formula for N, the number of bacteria t hours after the start of the experiment, assuming that N is an exponential function.

1.B Let g(x) = 500e.^.06x.Write the inverse of g and specify its domain.

1C. For an investment to double in 20 years, what is the percentage rate of growth(to the nearest percent) necessary? ] Use P = e^rt

1.D. An isotope has a half-life of 7 hours, how much will be left after one day?

Answer 1

(A)

we can use formula

At t=5, N(5)=700:

we can plug it

At t=9, N(9)=1200:

we can plug it

we can divide both equation

now, we can solve for k

now, we can find No

now, we can plug back

and we get

.............Answer

(B)

we are given

Inverse:

we can set g(x)=y

now, we can switch x and y

we can solve for y

now, we can take ln

so, we get

.............Answer

Domain:

Since, it is exponentially increaing function

initial value is 500

so, domain will be

(C)

we can use formula

at t=20, P(t)=2Po

now, we can solve for r

so,

growth rate is 3.465%..........Answer

(D)

we can use half life formula

we are given

h=7

we can plug it

One day means t=24

so, 9.287% of initial quantity is left........Answer