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Y_Kistochka [10]
3 years ago
12

Jorge is attending college next year. He just got information on the college costs and the financial aid package the college is

Mathematics
1 answer:
Ksivusya [100]3 years ago
8 0

Answer:the answer is 11,500.

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If f(x)f(x) is an exponential function where f(1.5)=5f(1.5)=5 and f(7.5)=79f(7.5)=79, then find the value of f(3)f(3), to the ne
stiv31 [10]

Answer: 7.93

Step-by-step explanation:

Given

f(x) is an exponential function. Suppose f(x) is ae^{bx}

f(1.5)=5\ \text{and}\ f(7.5)=79

\Rightarrow 5=ae^{1.5b}\\\Rightarrow \ln 5=\ln a-1.5b\quad \ldots(i)

Similarly,

\Rightarrow 79=ae^{7.5b}\\\Rightarrow \ln(79)=\ln a+7.5b\quad \ldots(ii)

Subtract (i) and (ii)

\Rightarrow \ln (79)-\ln (5)=9b\\\Rightarrow \ln (\frac{79}{5})=9b\\\\\Rightarrow b=\dfrac{\ln (\frac{79}{5})}{9}\\\\\Rightarrow b=0.3066

Insert the value of b

\Rightarrow 5=ae^{0.46}\\\Rightarrow a=5\times 0.6312\\\Rightarrow a=3.156\approx 3.16

So, the function becomes

\Rightarrow f(x)=3.16e^{0.3066b}

\Rightarrow f(3)=3.16e^{0.3066\times 3}\\\Rightarrow f(3)=7.927\approx 7.93

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