How many years will it take for an initial investment of$20,000to grow to$50,000?

Assume a rate of interest of 4% compounded continuously

It will take about howyears for the investment to grow to$50,000.

(Round to two decimal places asneeded.)

What will a $80,000house cost5years from now if the price appreciation for homes over that period averages 6% compounded annually?

The future cost of the house will be $

The size P of a certain insect population at time t (in days) obeys the functionP(t)=400e0.03t.

(a)Determine the number of insects att = 0days.

(b)What is the growth rate of the insectpopulation?

(c)What is the population after 10 days?

(d)When will the insect population reach 520?

(e)When will the insect population double?

Strontium 90 is a radioactive material that decays according to the functionA(t)=A0e0.0244t,

whereA0is the initial amount present and A is the amount present at time t (in years). Assume that a scientist has a sample of800grams of strontium 90.

(a)What is the decay rate of strontium 90?

(b)How much strontium 90 is left after 2020years?

(c)When will only600grams of strontium 90 be left?

(d)What is thehalf-life of strontium90?

The population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to answer parts(a)throughc).

(a) If N is the population of the colony and t is the time in days, express N as a function of t. ConsiderN0

is the original amount at t=0 and k0 is a constant that represents the growth rate.

N(t)=

The half-life ofcarbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only63% of thecarbon-14 expected in living matter, when did the tree die?

The tree died aboutyears ago.

A pizza pan is removed at 5:00 PM from an oven whose temperature is fixed at450Finto a room that is a constant70F.After 5 minutes, the pizza pan is at300F.

(a) At what time is the temperature of the pan130F?

(b) Determine the time that needs to elapse before the pan is160.

(c) What do you notice about the temperature as time passes?