The population of bedbugs is known to increase exponentially if left untreated. In one recent residence, PCO modelled the bedbug population using the function P(t) = 48(2), where P(t) is the number of bedbugs and t is the time in days. Algebraically determine how long will it take for the population to reach 312 bugs. Express your answer to the nearest tenth. (A) t=0.4 (B) t=2.6 (C) t=12.4 (D) 1=18.9

Suppose that P dollars in principal is invested in an account earning 3.4% interest compounded continuously. At the end of 5 yr, the amount in the account has earned $1760.40 in interest. Part: 0 / 2 Part 1 of 2 (a) Find the original principal. Round to the nearest dollar. (Hint: Use the model A = Pert and substitute P+1760.40 for A.) The original principal was approximately 9500 X Part: 1 / 2 Part 2 of 2 (b) Using the original principal from part (a) and the model A = Pet, determine the time required for the investment to reach $11,500. Round to 1 decimal place. Using the original principal from part (a) and the model A = Pe, it will take the investment approximately yr to reach $11,500.

A national census bureau predicts that a certain population will increase from 35.3 million in 2000 to 64.3 million in 2060. Complete parts (a) through (c) below. (a) Find an exponential function of the form f(t) = y₁b¹ for these data, in which t= 0 corresponds to 2000 and f(t) is in millions. f(t) (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (b) What is the projected population in 2030? In 2040? = In 2030, the population is projected to be (Round to one decimal place as needed.) million. million. In 2040, the population is projected to be (Round to one decimal place as needed.) (c) By experimenting with different values of t (or by using a graphing calculator to solve an appropriate equation), estimate the first full year in which the population will exceed 56 million. The first full year in which the population will exceed 56 million is

If f(x) is an exponential function, where f(-4) = 1 and f(4) = 69, then find the value of f(6.5) to the nearest hundredths. I asked this question before but the previous responder stated in his/her step 2 answer that  b8=69 but then wrote that b=(69)1/4 and this seems incorrect to me. Can you please re-do this problem?