Pre-Calculus

posted by .

The exponential function y(x)=Ce^ax satisfies the conditions y(0)=6 and y(1)=7.

(a) Find the constants C and a. Enter the exact value of a.
(b) Find y(2). Enter the exact answer. Simplify the answer so it does not contain any logarithms.

  • Pre-Calculus -

    6 = Ce^0
    C = 6

    7 = 6e^a
    a = ln(7/6)

    y(x) = 6e^(ln(7/6)x) = 6(e^(ln(7/6)))^x = 6*(7/6)^x
    y(2) = 6(7/6)^3 = 343/36

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calculus-check answers

    If cos theta = 0.8 and 270<theta<360, find the exact value of sin 2theta a) -0.96 b) -0.6 c) 0.96 d) 0.28 Answer: b 2) If csc theta = -5/3, and theta has its terminal side in Quadrant III, find the exact value of tan 2theta a)24/25 …
  2. math statistics

    For each probability and percentile problem, draw the picture. A random number generator picks a number from 1 to 9 in a uniform manner. 1) Give the distribution of X. X = 2) Enter an exact number as an integer, fraction, or decimal. …
  3. pre-calculas

    Find the slant asymptote, if any, of the rational function. Do not graph the function. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) f(x) = x2 − 2x + 15 _____________ x + …
  4. calculus

    Find the interval [a, b] on which the function f(x) = 2 x3+3 x2−12 x+3 is decreasing. Enter your answer as: [a, b] for some constants a, b.
  5. Calculus URGENT

    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = √x [0, 9] c=?
  6. Calc 1

    Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=?
  7. Calc 1

    Consider the following function. f(x) = x^6 ln x (a) Use l'Hospital's Rule to determine the limit as x → 0+. (b) Use calculus to find the minimum value. Find the interval where the function is concave up. (Enter your answer in …
  8. MathematicalModels

    Consider the Black-Scholes-Merton model for two stocks: dS1(t)=0.1S1(t)dt+0.2S1(t)dW1(t) dS2(t)=0.05S2(t)dt+0.1S2(t)dW2(t) Suppose the correlation between W1 and W2 is 0.4. Consider the dynamics of the ratio S1/S2, where A,B,C,D,F,G,I,J,K,L …
  9. Calculus 1

    Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = sqrt(x), [0,16]
  10. Calculus 1

    Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum …

More Similar Questions